Matthew constructs a fence around a patch of grass in his backyard. The patch has a width that is 8 feet more than 4 times the length. What is the perimeter of the fence if Matthew's patch of grass has an area of 5,472 square feet?

P=380 ft.

Explanation:

Area=length x width

Perimeter = 2*length + 2*width

Width = 4*length + 8

A=5472 ft²

5472 = l * (4l + 8) (plug in values)

5472 = 4l² + 8l (simplify)

4l² + 8l - 5472 = 0 (subtract 5472)

4 (l² + 2l - 1368) = 0 (factor out a 4)

4 (l + 38) (l-36) = 0 (factor)

l=36 ft. (-38 is extraneous because it is negative)

5472=38*w

w=152 ft.

P=2 (38) + 2 (152)

P = 380 ft.