Question

He length of a rectangle is five times its width.

If the perimeter of the rectangle is 120m , find its length and width.

Answer 1

Lets denote our variables as:

• x the width of the rectangle
• 5x the length of the rectangle

The formula for the perimeter of a rectangle is P = 2L + 2W, where L is the length of the rectangle and W is the width of the rectangle. We know that the perimeter of the rectangle is 120m, so we can write:

2(x) + 2(5x) = 120

2x + 10x = 120

12x = 120

x = 120/12

x = 10 m → Width of the rectangle

Substituting in the length:

5x = 5(10) = 50 m → Length of the rectangle

The length of the rectangle is 50 m and its width is 10 m.

Answer 2

w = 10

l = 50

Explanation:

Formula of Perimeter: w + w + l + l or 2w + 2l

l = 5w

2l + 2w = 120

2(5w) + 2w = 120

10w + 2w = 120

12w = 120

w = 10

l = 5(10)

l = 50

Check:

2l + 2w = 120

2(50) + 2(10) = 120

100 + 20 = 120

120 = 120

Hope This Helps!