Question

A rectangular exercise mat has a perimeter of 36 feet . The length mat is twice the width. Write and solve an equation to determine the length,in feet, of the the mat. Then find the area, in square feet, of the mat.

Answer 1

ANSWER

72 square feet

EXPLANATION

The perimeter of a rectangle is given by:

P= 2l+2w

It was given that, the perimeter of the rectangular mat, is 36 feet.

36= 2l+2w

Divide through by 2.

$18 = l + w...(1)$

It was given also that, the length of the mat is twice its width.

This implies that,

$l = 2w ...(2)$

Put equation (2) into equation (1) to get,

$18 = 2w + w$

$18 = 3w$

$w = 6 \: ft$

This means that the length is 12 ft.

The area of the rectangular mat is

$A = l \times w$

$A = 6 \times 12 = 72 {ft}^{2}$