A rectangular pool measures 12 feet by 20 feet. A patio of uniform width is built around the pool. The area of both the pool and the patio together is 560 square feet. Find the width of the patio.

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  1. dimensions of pool including the patio is (12+2x) by (20 + 2x), where x is the width of the patio around the pool

    (12+2x)(20+2x) + 12(20) = 560
    240 + 24x + 40x + 4x^2 + 240 - 560 = 0
    4x^2 + 64x - 80 = 0
    x^2 + 16x - 20 = 0

    solve using the quadratic formula since it doesn't factor.

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