# Perimeter of a rectangle

Finding the perimeter of a rectangle when the length and the width are given and finding the length or the width when the perimeter is given are the goals of this lesson. Start with the rectangle below and label the width w and the length l. Given a rectangle with side length (l) and width (w), the perimeter (P) or distance around the outside of the rectangle can be found by doing

P = l + w + l + w = 2 × l + 2 × w

Example #1:

Find the perimeter of a rectangle when l = 5 cm and w = 3 cm

P = 2 × 5 + 2 × 3

P = 10 + 6

P = 16

Notice that it is perfectly ok to do P = 5 + 3 + 5 + 3 = 8 + 8 = 16

However, it is usually easier and quicker to multiply each dimension by 2 and adding the result.

Example #2:

Find the perimeter of a rectangle when l = 9 cm and w = 5 cm

P = 2 × 9 + 2 × 5

P = 18 + 10

P = 28

Example #3:

Find the perimeter of a rectangle when l = 2/4 cm and w = 3/6 cm

P = 2 × 2/4 + 2 × 3/6

P = 2/1 × 2/4 + 2/1 × 3/6

P = (2 × 2)/(1 × 4) + (2 × 3)/(1 × 6)

P = 4/4 + 6/6

P = 1 + 1 = 2 cm

Example #4:

A rectangle has a perimeter of 14 inches. Find the length of the rectangle if the width is 4 inches

Here, given the perimeter and the width, you are asked to find the length of the rectangle.

We know that P = 2 × l + 2 × w

You should replace P by 14 and w by 4 because that is what they gave you.

So, 14 = 2 × l + 2 × 4

14 = 2 × l + 8

The problem becomes a two step equations that you need to solve

However, you can solve this equation with mental math. Just say to yourself, " 8 plus what equal 14? "

Since 8 + 6 = 14, 2 × l must equal 6

Ask yourself now, " 2 times what equal 6? "

Since 2 times 3 is 6, l = 3

Example #5:

A rectangle has a perimeter of 18 inches. Find the width of the rectangle if l is 5 inches

Here, given the perimeter and the length, you are asked to find the width of the rectangle.

We know that P = 2 × l + 2 × w

You should replace P by 18 and l by 5 because that is what they gave you.

So, 18 = 2 × 5 + 2 × w

18 = 10 + 2 × w

Again, the problem is a two step equations that you need to solve

However, you can solve this equation with mental math. Just ask yourself, " 10 plus what equal 18? "

Since 10 + 8 = 18, 2 × w must equal 8

Ask yourself now, " 2 times what equal 8? "

Since 2 times 4 is 8, w = 4

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!