# How to Find the Perimeter of a Rectangle: Formula & Example

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• 0:05 What Makes a Rectangle…
• 0:55 A Rectangle's Perimeter
• 2:12 Math Problem: Late for…
• 3:40 Math Problem: Exploring a Room
• 4:23 Math Problem: Annie's Bedroom
• 5:38 Lesson Summary

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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you'll review the properties of a rectangle. Then you'll learn how to find the perimeter of a rectangle. Afterward, you can test your knowledge with a brief quiz.

## What Makes a Rectangle a Rectangle?

Many of us know what rectangles look like, but what exactly makes a rectangle a rectangle?

To start off, all rectangles have four sides. But that alone doesn't make a rectangle. If that were the case, this would be a rectangle:

That, however, is a trapezoid -- definitely not a rectangle because in a rectangle, the four angles are all right angles.

Also, a rectangle's opposite sides are congruent, and when we say congruent, we mean they're of equal size.

We show congruence by marking the sides of equal length with the same number of hash marks as each other.

So a square is a type of rectangle because it has four sides with opposite sides congruent, and all its angles are right angles.

A square, however, has all four sides the same length, or congruent with each other, so we mark them with the same number of hash marks.

## A Rectangle's Perimeter

The perimeter of a rectangle is equal to the sum of all the sides. However, since a rectangle's opposite sides are congruent, we only need to know the length and width.

We can write this in an equation this way:

P = l + w + l + w

where P is the perimeter, l is the length of the rectangle and w is its width. But instead of writing the l and w twice, we can simplify the equation like this:

P = 2l + 2w

What if we were given the following measurements?

This rectangle has a length of 6 inches and a width of 3 inches. We can still calculate the rectangle's perimeter because we know that the other two sides also measure three and six inches, respectively.

So, we plug in 6 for l and 3 for w in our equation, and we have

P = 2(6) + 2(3) = 18

This rectangle's perimeter is 18 inches.

What if we were given the measurements for these two sides?

The image tells us that this rectangle's length is 4 feet, but we know nothing about its width. Even though we're given two sides, they're not the length and the width, both of which we need to determine perimeter. So we can't calculate this rectangle's perimeter from the information given.

## Math Problem: Late for Practice

Sammy was late to football practice, so his coach is making him run around the entire field three times. The field, including the end zones and the practice area behind the end zones is 160 yards long and 53 yards wide. What's the total distance Sammy has to run?

Well, since Sammy is running along all sides of the rectangular field, we're dealing with perimeter here.

Let's make a diagram of the field:

This rectangle has a length of 160 yards and a width of 53 yards. We have the information we need to plug into our perimeter formula.

P = 2l + 2w

Plugging in 160 for l and 53 for w, we have:

P = 2(160) + 2(53)

Multiplying 2 times 160 gives us 320, and multiplying 2 times 53 gives us 106, so we now have:

P = 320 + 106

We add 320 plus 106 and get:

P = 426

The field's perimeter is 426 yards.

Since Sammy has to run around the field three times, we'll need to multiply the perimeter by 3:

426 x 3 = 1,278

Sammy has to run 1,278 yards! He'd better get started!

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