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.

Answer 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.