Question

You have a pool that measures 8 yards by 10 yards. You want to build a deck around all four sides of the pool and you want to increase the total area to 120 square yards. The deck is the same width on both sides forming a perfect rectangle. What is the width of the deck?

Answer 1

Given:
pool length : 10 yards
pool width : 8 yards

Area = 10 yds * 8 yds = 80 yd²

(10 + 2x)(8 + 2x) = 120 
10(8 + 2x) + 2x(8+2x) = 120
80 + 20x + 16x + 4x² = 120
4x² + 36x + 80 - 120 = 0
4x² + 36x - 40 = 0
4(x² + 9x - 10) = 0
4(x + 10)(x - 1) = 0

x + 10 = 0
x = -10
x - 1 = 0 
x = 1

the width of the deck is 1 yard