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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

rectangle-image

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 dimenssion 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 = 3



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