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8 May, 20:57

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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  1. 8 May, 21:16
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    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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