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22 March, 13:30

An in ground rectangular pool has a concrete pathway surrounding the pool. if the pool is 16 feet by 32 feet and the entire area of the pool including the walkaway is 924 ft^2, find the width of the walkway

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  1. 22 March, 14:12
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    1. Let's call:

    x: the width of the walkway.

    b: 2x+16 (there is a widht "x" of the walkway on each side).

    h: 2x+32 (there is a widht "x" of the walkway on each side).

    A: 924 ft^2 (the area of the pool of including the walkway).

    2. The area of a rectangle is:

    A = (b) (h)

    b: the base of the rectangle (2x+16)

    a: the height of the rectangle (2x+32)

    3. Then, we have a quadratic equation:

    924 = (2x+16) (2x+32)

    4x^2+64x+32x+512-924=0

    4x^2+96x-412=0

    4. We apply the quadratic formula to find the value of "x":

    x = (-b±√ (b^2-4ac)) / 2a

    x=3.71

    The answer is: The width of the walkway is 3.71 ft
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