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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?

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Answer:

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.

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