### Perimeter of a Rectangle

#### Lesson Objective

In this lesson, we will learn about the perimeter of a rectangle.

#### About This Lesson

In this lesson, we will:

- Learn about the perimeter of a rectangle and derive the formula for finding its perimeter.
- See an example on using the formula to find the perimeter.
- See another example on using the formula to find the length of a rectangle.

The study tips and math video below will explain more.

### Study Tips

#### Tip #1

A rectangle has four right angles. The sides of a rectangle that are opposite each other have the same length.

Now, if a rectangle has the length of l and the width of w, its perimeter, P, will be the total distance around the outside of the rectangle. Hence:

P = 2(l+w)

The math video below will give more explanation on this. Also, we will see some examples on how to use this formula.

### Math Video

#### Video on the perimeter of a rectangle

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#### Math Video Transcript

PART 1

00:00:04.000

In this lesson, we will learn about the perimeter of a rectangle.

00:00:09.030

Consider this rectangle. This rectangle has the length of L and the width of W.

00:00:17.000

Since, the perimeter of the rectangle, P, is the total distance around the outside of the rectangle, the perimeter, will be equals to L, add with W, add with another L, and finally, add with another W.

00:00:39.020

Let's simplify this. L add with L, gives 2L. Similarly, W add with W, gives 2W.

00:00:52.110

Notice that, these two terms have '2' as a common factor.

00:00:58.140

Hence, by taking out '2', we have, 2(L+W).

00:01:06.070

Therefore, the perimeter, P = 2(L+W).

00:01:15.000

Let's rewrite it here.

00:01:18.100

Note that, in any calculation, when we found the value of P, it is important to include the unit.

00:01:26.140

For example, if L and W are given in centimeter, the unit for the perimeter will be in centimeter as well.

00:01:35.230

The next video will show some examples on using this formula.

#### Video on the examples on using the formula P=2(l+w)

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#### Math Video Transcript

PART2

00:00:04.020

After understanding the formula for the perimeter of a rectangle, let's see some examples on using the formula.

00:00:12.080

Find the perimeter of this rectangle, when its length is 4cm, and its width is 3cm.

00:00:20.010

We start with the formula for the perimeter of a rectangle, P=2(L+W).

00:00:29.060

Since the length of the rectangle is given as 4cm, we can substitute, L with 4.

00:00:37.070

Similarly, since the width is given as 3cm, we can substitute W with 3.

00:00:45.060

Let's simplify this. 4 add with 3, gives 7. 2 multiply with 7, gives 14.

00:00:57.110

Hence, we have P=14.

00:01:02.210

Now, this number doesn't mean anything, unless we include the unit for it.

00:01:09.060

Since the length, and the width, are given in centimeter, the unit for the perimeter will also be in centimeter.

00:01:17.110

Therefore, the perimeter of this rectangle is equals to 14cm.

00:01:25.050

Next example, the perimeter of this rectangle, is 24ft, and its width is 5ft. Find its length.

00:01:37.060

Again, we start with the formula for the perimeter of a rectangle, P=2(L+W).

00:01:46.030

Since the perimeter, and the width of the rectangle are given, we can find the length of the rectangle, by solving this equation for L.

00:01:56.080

Let's start. The perimeter is given as 24ft. Therefore, we can substitute P with 24.

00:02:08.210

Similarly, since the width is given as 5ft, we can substitute W with 5.

00:02:17.150

Now, to get a step closer in finding L, we need to remove '2'.

00:02:24.110

To do so, we divide both sides of the equation with 2. This gives, 24 over 2, equals to L plus 5.

00:02:37.020

24 divided by 2, gives 12.

00:02:41.150

Now, we have, L plus 5, equals to 12.

00:02:48.030

Let's rewrite this equation so that it looks neater.

00:02:52.170

Next, to find L, we need to remove 5. To do so, we add -5 to both sides of the equation.

00:03:03.090

By doing so, we get, L equals to 12 minus 5. 12 minus by 5, gives 7.

00:03:13.170

Now, we have, L equals to 7. Note that, this number doesn't mean anything, unless we include the unit for it.

00:03:25.110

Since the width is in feet, the length will also be in feet.

00:03:31.050

Finally, the length of this rectangle is 7ft.

00:03:37.110

That is all for this lesson. Try out the practice question to further your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the perimeter of a rectangle or pick your choice of question below.

- Question 1 on finding the perimeter of a rectangle
- Question 2 on finding the width of each side of a rectangle

#### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.