problem solving involving length

Length Problems

Length word problems.

Example 1: A 57-foot wood is cut into two pieces. One piece is 3 feet less than twice the length of the other. What is the length of the longer piece of wood?

Just like in any other kind of word problem, the first step that we have to do is to identify what important pieces of information are given to us in the problem.

In this example, we are told how long the wood is (57 feet) as well as the measurement for one of the two pieces. The given piece is defined using the other piece so let’s call it the second piece and assign the variable [latex]\large{x}[/latex] to represent the first piece. Note that the measurement of the first piece is currently unknown.

Since the second piece is 3 feet less than twice the length of the first piece , then it can be algebraically expressed as [latex]2{\large{x}} – 3[/latex].

So we have,

• Total Length: [latex]57[/latex]
• First Piece: [latex]\large{x}[/latex]
• Second Piece: [latex]2{\large{x}}-3[/latex]

Now that we have all this information, let’s go ahead and solve for [latex]\large{x}[/latex] so we can find the measurements for both pieces.

Luckily for length word problems, we don’t have to remember any particular formula. We simply have to set up our equation where we add all the pieces on one side and the total length of the object on the other.

First Piece + Second Piece = Total Length

Let’s solve for [latex]\large{x}[/latex].

Going back to our original problem, it asks us for the measurement of the longer piece. At this point, we only know that the first piece is 20 feet long. In order to determine which one is longer, we’ll use the value of [latex]\large{x}[/latex] to also find the length of the second piece. Therefore,

• First Piece = [latex]20[/latex]
• Second Piece = [latex]2x-3[/latex] = [latex]2({\color{red}20}) – 3[/latex] = [latex]40-3[/latex] = [latex]37[/latex]

Answer: The longer piece of wood is 37 feet long.

Before we move on to the next problem, let’s do a quick check to make sure that we got the correct answers. We were told that the total length of the wood is 57 feet. So we’ll check if the measurements of our pieces indeed sum up to 57.

And it did! With this quick check, we were able to verify that the measurements we got for both pieces are correct.

Example 2: A wire is cut into two pieces. The shorter piece is 1 meter more than half the longer piece. The length of the wire is 28 meters. What is the measure of the shorter piece?

This next example is quite similar to the first one. Right away, we can see that the shorter wire is defined using the length of the longer wire. The length of the longer wire at this point is unknown, so let’s use the variable [latex]L[/latex] to represent it.

So what do we have?

• Total Length: [latex]28[/latex]
• Longer Piece: [latex]L[/latex]
• Shorter Piece: 1 meter more than half the longer piece → [latex]{\Large{{L \over 2}}} + 1[/latex]

Let’s now proceed to solve for [latex]L[/latex] by adding the longer piece and the shorter piece then set it equal to the total length of the wire. So we have,

Longer Piece + Shorter Piece = Total Length

Great! We now know that our longer piece is 18 feet long. But since the problem is asking for the measurement of the shorter piece, we’ll use the value of [latex]L[/latex] which is [latex]18[/latex], to also find out how long the shorter piece is.

• Longer Piece: [latex]18[/latex]
• Shorter Piece: [latex]{\Large{{L \over 2}}} + 1[/latex] = [latex]{\Large{{{\color{red}18} \over 2}}} + 1[/latex] = [latex]9+1[/latex] = [latex]10[/latex]

Answer: The length of the shorter piece of wire is 10 meters.

To verify, let’s add both of the pieces to see if they equal the total length of the wire which is 28 meters.

Example 3: A piece of board is cut into three segments. The second segment is 3 inches more than the first segment. The third segment is twice as long as the second segment. If the board is 117 inches, what is the length of the third segment?

Here we have an object that is divided into three. As you can see, the 2nd segment is described in terms of the measurement of the 1st segment while the 3rd segment is defined using the length of the 2nd segment. How about the 1st segment? Well, this segment is unknown right now so let’s represent it with the variable [latex]F[/latex].

Looking back at our word problem, here are the information that we have so far.

• Total Length: 117
• First Segment: [latex]F[/latex]
• Second Segment: 3 inches more than the 1st segment → [latex]F+3[/latex]
• Third Segment: twice as long as the 2nd segment → [latex]2(F+3)[/latex]

We’ll proceed by setting up our equation and solving for [latex]F[/latex].

1st Segment + 2nd Segment + 3rd Segment = Total Length

As you know, we used the variable [latex]F[/latex] to represent the 1st segment of the board. Therefore, we can say that the 1st segment is 27 in. long. Since our problem is asking us to find how long the 3rd segment is (which is currently defined using the 2nd segment), this means that we also have to find the measurements of both the 2nd and 3rd segments.

• 1st Segment: [latex]27[/latex]
• 2nd Segment: [latex]F+3[/latex] = [latex]{\color{red}27}+3[/latex] = [latex]30[/latex]
• 3rd Segment: [latex]2(F+3)[/latex] = [latex]2({\color{red}30})[/latex] = [latex]60[/latex]

Answer: The length of the third segment is 60 inches.

Let’s do a quick check if all the segments, when added, will give us the total length of the board which is 117 inches.

Example 4: A stick is broken into three pieces. The second piece is twice the length of the first piece. The third piece is the average of the first piece and the second piece. The length of the stick is 207 centimeters. Which among the pieces has a measurement that is between the shortest and the longest piece and what is its dimension?

This problem is quite interesting and I must say, is packed with a lot of information. However, do not let that overwhelm you. As long as you continue to follow the steps that we’ve been doing in our previous examples, you’ll realize that this problem isn’t as hard as it looks.

What details are given to us?

• Total Length: [latex]207[/latex]
• 1st Piece: [latex]\large{x}[/latex]
• 2nd Piece: twice the length of the first piece → [latex]2{\large{x}}[/latex]
• 3rd Piece: the average of the first piece and the second piece → [latex]\Large{{{x + 2x} \over 2}}[/latex]

As you can see, we used the variable [latex]\large{x}[/latex] to stand for the first piece which is currently unknown, because it is not defined using the second piece nor the third piece.

Our next step is to solve for [latex]\large{x}[/latex].

Using the value of [latex]\large{x}[/latex], let’s find out how long each piece of the broken stick is.

• 1st Piece: [latex]46[/latex]
• 2nd Piece: [latex]2x[/latex] → [latex] 2({\color{red}46})[/latex] → [latex]92[/latex]
• 3rd Piece: [latex]\Large{{{x + 2x} \over 2}}[/latex] → [latex]\Large{{{{\color{red}46} + {\color{red}92}} \over 2}}[/latex] → [latex]\Large{{{138} \over 2}}[/latex] → [latex]69[/latex]

Going back to our original question…which among the pieces has a measurement that is between the shortest and the longest piece, and what is its dimension?

Answer: The third piece of the stick which is 69 centimeters long has the measurement that is between the shortest and the longest pieces.

This time, I’ll leave it up to you to check if the measurements that we got for the three pieces indeed sum up to 207 cm.

Example 5: A rope is cut into two pieces. If the first piece is added to the second piece, the sum is 25 yards. In addition, twice the first piece plus the second piece equals 40 yards. What is the measure of the shorter piece?

Now this problem is a little tricky. If you notice, none of the two pieces are described in terms of the other.

To start, let us identify the pieces of information that are given in the problem and translate each statement algebraically into an equation.

Let’s use the variables [latex]F[/latex] and [latex]S[/latex] to represent the first piece and second piece, respectively.

1) If the first piece is added to the second piece, the sum is 25 yards .

[latex]F + S = 25[/latex]

2) Twice the first piece plus the second piece equals 40 yards .

[latex]2F + S = 40[/latex]

Going through both statements, we are able to come up with two equations.

• Equation 1: [latex]F + S = 25[/latex]
• Equation 2: [latex]2F + S = 40[/latex]

As you can see, we are dealing with two equations with two unknowns, [latex]F[/latex] and [latex]S[/latex] which means we will be solving systems of linear equations with two variables.

Our next step is to use Equation 1 to express the second piece ([latex]S[/latex]) in terms of the first piece ([latex]F[/latex]). Then we can substitute the expression that we get into Equation 2. In doing so, we will have a multi-step equation with only [latex]F[/latex] as the only variable instead of having both.

Note that we can also do the other way around. That is, expressing the first piece in terms of the second piece. However, for this example, we’ll solve for the variable [latex]S[/latex].

We’ll do this step-by-step so it’s easy to understand and follow.

1) Start with Equation 1. Solve for [latex]S[/latex].

2) Next, substitute the expression of [latex]S[/latex] into Equation 2.

Remember that the variable [latex]F[/latex] stands for the first piece. Therefore, we can now say that the first piece is 15 yards. However, since our problem is asking us for the measure of the shorter piece, we also need to find how long the second piece is, so we can compare and identify between the two (1st piece and 2nd piece) which one is shorter.

• First Piece: [latex]15[/latex] yards
• Second Piece: [latex]10[/latex] yards

We now know that the second piece then is the shorter piece. Let’s go ahead and answer the original question.

Answer: The shorter piece is 10 yards long.

In order to verify that our answers are correct, we’ll substitute the values of [latex]F[/latex] and [latex]S[/latex] into both Equations 1 and 2. In doing so, we’ll be able to prove that the statements given in the word problem are true.

Example 6: A piece of wood is cut into two. The sum of the first piece and the second piece is 71 inches. The difference of 4 times the first piece and twice the second piece is 20 inches. What is the measure of the longer piece?

This one is similar to what we just discussed in Example 5. Since neither of the two pieces is defined in terms of the other piece, let’s look at the important pieces of information that are given to us in the problem.

Like our previous example, we’ll examine each of the statements first then translate them algebraically.

Let [latex]\large{x}[/latex] be the first piece and [latex]\large{y}[/latex] be the second piece.

1) The sum of the first piece and the second piece is 71 inches .

Equation 1: [latex]\large{x + y = 71}[/latex]

2) The difference of 4 times the first piece and twice the second piece is 20 inches .

Equation 2: [latex]\large{4x – 2y = 20}[/latex]

Now that we have our two equations, let’s express the first piece ([latex]\large{x}[/latex]) in terms of the second piece ([latex]\large{y}[/latex]).

• Using Equation 1, let’s solve for [latex]\large{x}[/latex]. So we have,

• Substitute the expression of [latex]\large{x}[/latex] into Equation 2.

Looking back at our original problem, it’s asking us for the measure of the longer piece. At this point, we know that the second piece ([latex]\large{y}[/latex]) is 44 in. long. But is it the longer piece? Well, we don’t know yet. We have to know how long the first piece ([latex]\large{x}[/latex]) as well so we can determine which one is longer.

We already have our expression for [latex]\large{x}[/latex], so all we need to do is substitute the value of [latex]\large{y}[/latex] into the expression.

Okay, let’s do a recap. The measurements for our two pieces are:

• First Piece: [latex]27[/latex] in.
• Second Piece: [latex]44[/latex] in.

Perfect! Now we know that the second piece is longer than the first piece.

Going back to the original question, what is the measure of the longer piece?

Answer: The longer piece is 44 inches long.

Word Problems on Measuring Length

We will discuss here how to solve the word problems on measuring length (i.e. addition and subtraction).

Addition and subtraction in meters and centimeters is done in the similar way as in the case of ordinary numbers.

(i) When we add meters and meters the sum is in meters and when we add centimeters and centimeters the sum is in centimeters. Here centimeters are written as two digit number.

(ii) When we subtract meters from meters the difference is in meters and when we subtract centimeters from centimeters the difference is in centimeters. Here centimeters are written as two digit number.

Solved word problems on measuring length:

1.  Sita is 1 m 30 cm tall and her sister Rita is 1m 60 cm tall. Who is taller and by how much?

Rita is taller by 1 m 50 cm - 1 m 30 cm = 20 cm

2. Maria purchased 24 m 25 cm rope and Nancy purchased 17 m 15 cm rope. What is the total length of ropes both of them purchased?

Length of ropes purchased by Maria = 24 m 25 cm

Length of ropes purchased by Nancy = 17 m 15 cm

Total length of ropes purchased by them = 24 m 25 cm + 17 m 15 cm

                                                           = 41 m 40 cm

3. Subtract 20 m 15 cm from 36 m 95 cm.

First arrange meters and centimeters in columns.

Then subtract 15 cm from 95 cm.

4. Mary is 1 m 15 cm tall. Her friend Larry is 1 m 30 cm tall. Who is taller and by how much?

5. Aaron bought 9 m 75 cm of cloth. He used 2 m 30 cm from it. How much cloth is left?

Total length of cloth Aaron bought = 9 m 75 cm.

Length of cloth he used = 2 m 30 cm.

Therefore, the length of cloth left = 9 m 75 cm - 2 m 30 cm

                                              = 7 m 45 cm

Measurement of Length:

Standard Unit of Length

Conversion of Standard Unit of Length

Addition of Length

Subtraction of Length

Addition and Subtraction of Measuring Length

Addition and Subtraction of Measuring Mass

Addition and Subtraction of Measuring Capacity

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Solving problems involving height and length

Part of Maths Measuring Year 2

Watch: Estimating and measuring

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Fin and Snoot calculate the length of their new cars, using feet, centimeters and meters.

Video Transcript Video Transcript

NARRATOR: Hello Snoot, what’s that you’re driving?

ALIEN: (Alien language)

NARRATOR: I see, you hired a go-kart from the intergalactic market.

Hello Finn.

NARRATOR: What an impressive car. On Earth, that’s called a limousine. It’s a lot longer than Snoot’s go-kart isn’t it?

How long is it exactly?

NARRATOR: I’ve got an idea, you can estimate the length in steps.

The go-kart is ten steps in length and the limousine is 30 steps in length.

30 is three times ten. That makes the limousine three times longer than the go-kart.

NARRATOR: I know Snoot. Counting things out in steps isn’t very accurate, it just gives you an estimate of how long things are.

If you want to know exactly, you’ll have to use a tape measure.

On Earth we use centimetres to measure quite small lengths, like the width of a tire, or the diameter of a wheel.

And we use metres to measure longer lengths, like the length of a car.

ALIENS: Ah ha!

NARRATOR: So, according to the tape measure, Snoot’s go-kart is two metres long, and Finn’s limousine is six metres long.

Six is three times two, so your estimates were right!

The limousine is three times longer than the go-kart.

Hello Plimble.

ALIEN: Hello.

NARRATOR: I see you hired a monster truck. I think we are going to need a bigger tape measure.

More on Measuring

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Measuring mass in grams

• count 6 of 10

Measuring mass in kilograms

• count 7 of 10

Measuring in millilitres

• count 8 of 10

Measuring in litres

• count 9 of 10

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Length word problems

Inches, feet, cm, m.

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Practice Length Measurement Problems

To solve length measurement problems , we need to have various factors in mind: the unit of measurement used, conversion exercises, and the understanding of how to use different measuring units. In this post, we’ll present different exercise types that’ll help us understand these concepts.

Unit of Measure Used to Express the Information

In problems that deal with length measurements, it’s extremely important to always have the unit that is used in mind. A length expressed in km is not the same thing as a length expressed in cm.

To stress the importance of this concept, it’s important to do exercises that make us approximate the measuring unit according to the length of the object that is being measured.

This is an example of a problem where we work on the approximation of measurements according to the unit in use.

These measurements don’t have to be exact because the exact measurement is not what we’re after. What’s important is that the student understands that, in this case, a palm can’t be measured in kilometers or meters, but rather, in the appropriate unit, or centimeters.

Understanding the Use of Different Measuring Units

It’s also important to show students the practicality of this lesson with problems where they have to apply what they’ve learned.

This is how we can teach the practicality of expressing each situation according to its corresponding unit of measure. It also helps you be more attentive to the differences so you can go ahead with changing the units necessary in order to solve the problem.

Conversion Length Measurement Problems

The problems that we’ve made for the application on unit conversion have to be realistic so that they teach students how to apply what they’ve learned in real life.

So, wrapping up, we maintain that in order to do exercises that require students to know length units, we must continue the learning process with different concepts that are implied by this topic in a progressive manner:

• The practicality of using different length and measuring unit multiples and submultiples.
• Making examples out of different real-life situations.
• Applying what was learned to real-life situations that require unit conversions. If you thought this post was interesting, remember that you can find more like this at  Smartick

Learn More:

• Learn to Solve Measuring Problems
• Conversion Capacity Problems in the Metric System
• Learn More about Measurements of Length
• Dimensions: Length, Width, and Height of an Object
• Review of All Units of Measurements
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Resources tagged with: Length/distance

There are 58 NRICH Mathematical resources connected to Length/distance , you may find related items under Measuring and calculating with units .

Car Journey

This practical activity involves measuring length/distance.

Can You Do it Too?

Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.

Olympic Measures

These Olympic quantities have been jumbled up! Can you put them back together again?

Now and Then

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

Olympic Starters

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

The Animals' Sports Day

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Order, Order!

Can you place these quantities in order from smallest to largest?

Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

A Question of Scale

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Sizing Them Up

Can you put these shapes in order of size? Start with the smallest.

Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Rolling Around

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Four on the Road

Four vehicles travel along a road one afternoon. Can you make sense of the graphs showing their motion?

Uniform Units

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Where Am I?

From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?

Lengthy Journeys

Investigate the different distances of these car journeys and find out how long they take.

Working with Dinosaurs

This article for teachers suggests ways in which dinosaurs can be a great context for discussing measurement.

Swimmers in opposite directions cross at 20m and at 30m from each end of a swimming pool. How long is the pool ?

Triangle Relations

What do these two triangles have in common? How are they related?

A Scale for the Solar System

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Flight Path

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Chippy's Journeys

Chippy the Robot goes on journeys. How far and in what direction must he travel to get back to his base?

Can you prove that the sum of the distances of any point inside a square from its sides is always equal (half the perimeter)? Can you prove it to be true for a rectangle or a hexagon?

Measure for Measure

This article, written for students, looks at how some measuring units and devices were developed.

Eclipses of the Sun

Mathematics has allowed us now to measure lots of things about eclipses and so calculate exactly when they will happen, where they can be seen from, and what they will look like.

A paradox is a statement that seems to be both untrue and true at the same time. This article looks at a few examples and challenges you to investigate them for yourself.

How can the school caretaker be sure that the tree would miss the school buildings if it fell?

N Is a Number

N people visit their friends staying N kilometres along the coast. Some walk along the cliff path at N km an hour, the rest go by car. How long is the road?

The Dodecahedron Explained

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

Do You Measure Up?

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

The Hare and the Tortoise

In this version of the story of the hare and the tortoise, the race is 10 kilometres long. Can you work out how long the hare sleeps for using the information given?

A Flying Holiday

Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.

Watching the Wheels Go 'round and 'round

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Nirmala and Riki live 9 kilometres away from the nearest market. They both want to arrive at the market at exactly noon. What time should each of them start riding their bikes?

Practice Run

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

A Rod and a Pole

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

How many centimetres of rope will I need to make another mat just like the one I have here?

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

On the Road

Four vehicles travelled on a road. What can you deduce from the times that they met?

Use your hand span to measure the distance around a tree trunk. If you ask a friend to try the same thing, how do the answers compare?

Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Solve problems involving length

I can solve problems involving length.

Lesson details

Key learning points.

• Data can be collected to help solve a problem involving length.
• When we collect data, we need to decide which units to measure in: mm, cm or m.
• Representing data as a bar graph can help us interpret the data.

Common misconception

Drawing tables and graphs from scratch can be tricky for some children.

Provide scaffolds of tables and graphs where necessary.

Data - Data is a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

Interpret - When we interpret anything, including data, we explain its meaning.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Starter quiz

6 questions.

Big Ben -  

Eiffel Tower -  

Blackpool Tower -  

Leaning Tower of Pisa -  

Pose a question or statement. -  

All famous towers are taller than 100 m.

Collect data. -  

Research into the heights of towers, given in metres.

Represent the data. -  

Draw a bar graph to compare their heights.

Interpret the data. -  

Do all the towers have bars that are taller than 100 m?

Measurement Word Problems (Grade 4)

Suggested learning targets.

• I can use +, -, ×, and ÷ to solve word problems.
• I can solve measurement word problems that include whole numbers, fractions, and decimals.
• I can convert larger units into equivalent smaller units to solve a problem.

The following activities are obtained from the Howard County Public School System. Activity 1: In PE, Zack and his friends had to measure their heights. They each used a different measurement tool, and then recorded their heights in the chart below.

Order the three boys by height, writing their names from tallest to shortest.

Explain how you figured out which boy was the tallest of the three.

A fourth student, Ryan, measured himself using a meter stick, and he found that he was exactly one meter tall.  If a meter measures approximately 39 inches, how does Ryan's height compare to the heights of the other three boys? Tell how Ryan compares in height to Zack, Duncan, and Cameron.  Then, use what you know about yards, feet, inches, and meters to explain your thinking.

Show on a number line the amount of time Jack and Abby each stayed underwater. How much longer could Abby stay underwater than Jack?

Coach Foster told the kids that he was a champion swimmer, and he used to train himself to hold his breath.  The longest he was ever able to hold his breath was three minutes.  How much longer would Abby have to hold her breath underwater to match Coach Foster's time?  Explain your thinking using words, numbers, and/or symbols.

Activity 3: Brandon and Kelly are training to run in a 5-kilometer race next month.  Each morning, Brandon runs a route through the neighborhood park while Kelly runs on the racetrack at the high school.

Explain how you know which person ran a longer distance.

On Wednesday, Kelly was able to run 9 laps, while Brandon ran 3 kilometers. How much further did Kelly run than Brandon on Wednesday? On Friday, Kelly ran a certain number of laps, and Brandon ran a certain number of kilometers.  They ended up running the same distance as each other.  How far could each of them have run?

Activity 4: Tyler has been saving up for a new video game that costs $60.  He earned $28.75 over the past two weeks by mowing lawns, and his grandmother sent him $25 for his birthday.¦nbsp; He knew he didn't have enough for the video game, so he decided to take the twenty half-dollar coins he had in his coin collection.

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Word Problems Involving Width, Length and Area

When you see a word problem, you know that you are going to have to extract the facts of the problem from the text. In order to make sure you understand the problem, you have to first be certain you understand all the words that are used, especially those involving math. If you can put into your own words what the problem is asking you to find, you are a good way towards being able to solve the word problem.

Once you've figured out what the word problem is asking, you must devise a plan to find the solution. You might want to look for a pattern, draw a diagram, set up variables to solve an equation, or something else. Follow through with the plan and then check to make sure your solution makes sense.

Width, length, and area

To find the area of a rectangle, we use the formula:

where A is the area, w is the width, and h is the height of the rectangle.

To find the area of a triangle, we use the formula:

A = 1 2 b h

where A is the area, b is the base of the triangle, and h is the height.

Word problems involving width, length, and area will frequently give you two of these measurements and require you to solve for the third measurement.

Word problems with rectangles

A city block, in the shape of a rectangle, is divided into 56 square plots of equal size. There are 14 plots along the length of the block. How many plots are there along the width of the block?

This problem involves area, and the unit used is one square plot. The area of the city block is 56, and the length of the block is 14. Substitute in the formula:

56 = w × 14

To solve this problem, you use the inverse operation of multiplication , which is division . Divide both sides by 14 to isolate the width.

56 14 = w × 14 14

w × 1 = 4

Therefore, w = 4 .

The width of the city block is 4 plots.

To check your answer, multiply 14 by 4, and you get 56. So your answer is correct.

Word problems with triangles

Maria is surveying a plot of land that is shaped like a right triangle. The area of the land is 45,000 square meters. If the bottom leg of the plot is 180 meters long, how long is the side leg of the triangular plot?

This is another area problem, this time using the formula to solve for the area of a triangle. Because it's a right triangle, one leg is considered the base and the other leg is considered the height. So we will substitute 45,000 for A (area) in the formula and 180 for b (base) in the formula.

45000 = 1 2 × 180 × h

First, we simplify the problem by multiplying 1 2 by 180.

45000 = 90 h

Then we isolate the h by dividing both sides by 90.

45000 90 = h

This lets us know that the second leg of the triangular plot is 500 meters long.

We can check our answer by multiplying 180 × 500 , which is 90,000, and multiplying that by 1 2 , which is 45,000. Our answer is correct.

Topics related to the Word Problems Involving Width, Length and Area

Word Problems

Flashcards covering the Word Problems Involving Width, Length and Area

4th Grade Math Flashcards

Common Core: 4th Grade Math Flashcards

Practice tests covering the Word Problems Involving Width, Length and Area

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4th Grade Math Practice Tests

Get help learning about word problems involving width, length, and area

Word problems of any kind can be especially challenging for some students. If your student needs help with word problems, specifically those involving width, length, and area, have them meet with a math tutor who can walk them through the steps and explain what's going on in a way that your student will understand. By going at your student's pace and using what they know about your student's learning style, a tutor can make their lessons as efficient and effective as possible. Contact Varsity Tutors and speak to one of our Educational Consultants today if you'd like to learn more about how tutoring can help your student understand word problems involving width, length, and area.

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Solving Word Problems Involving Lengths 2nd Grade Math Worksheets

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Definition:

A word problem is similar to a short story. It asks us to solve for something by changing the given phrases to number sentences to find the solution.

What should be know in solving for word problems ?

• What is given?
• What is asked?
• What operation should be used?
• What number sentence should be written
• What is the solution?

Steps to follow in solving word problems

• Read your problem carefully
• Draw a picture or a diagram
• Look for keywords as you read
• Write a number model or a number sentence
• Find the answer and write the correct unit

Janni brought 120 cm long cue before his training. After the training he realized that his cue is too long, so he brought 100 cm long cue on the next day of the training. What is the difference of first cue and the second cue?

• What is given? First Cue:120 cm Second Cue:100 cm
• What is asked? Difference of first and second cue
• What Operation should be used? Subtraction
• What number sentence should be written 120 – 100 = ?
• What is the solution? 120 cm – 100 cm = 20 cm

*The difference of first and second cue is 20 cm.

Solving Word Problems Involving Lengths Worksheets

This is a fantastic bundle which includes everything you need to know about Solving Word Problems Involving Lengths across 15+ in-depth pages. These are ready-to-use Common core aligned Grade 2 Math worksheets .

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