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.
[tex]18 = l + w...(1)[/tex]
It was given also that, the length of the mat is twice its width.
This implies that,
[tex]l = 2w ...(2)[/tex]
Put equation (2) into equation (1) to get,
[tex]18 = 2w + w[/tex]
[tex]18 = 3w[/tex]
[tex]w = 6 \: ft[/tex]
This means that the length is 12 ft.
The area of the rectangular mat is
[tex]A = l \times w[/tex]
[tex]A = 6 \times 12 = 72 {ft}^{2} [/tex]
