Question

The length of a rectangle is 2 more than 3 times its width. If the perimeter is 68, find the length and width.

Answer 1

The length is 26 and the width 8.

Explanation:

First you have to consider that the perimeter of a rectangle = 2·length + 2width. If length = 3width + 2, you can call "x" to the width. Then

x = width ⇒ length = 3x + 2.

Perimeter = 2·(3x + 2) + 2·x ⇒ Perimeter = 6x + 4 + 2x ⇒

Perimeter = 8x + 4 ⇒ 68 = 8x + 4 ⇒ 68 - 4 = 8x ⇒ 64 = 8x ⇒ 64/8 = x

⇒ x = 8.

Finally, width = 8 and length = 3x + 2 ⇒ length = 26