A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the deck around the pool?
Let the width of the deck be x feet.
The total area of the deck is given by:
Total area = (20+2x)(50+2x) - 20*50
456 = (20+2x)(50+2x) - 1000
456 = 1000 + 40x + 100x + 4x^2 - 1000
456 = 40x + 100x + 4x^2
456 = 140x + 4x^2
4x^2 + 140x - 456 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
x = (-140 ± √(140^2 - 4*4*(-456))) / 2*4
x = (-140 ± √(19600 + 7296)) / 8
x = (-140 ± √26896) / 8
x = (-140 ± 164) / 8
x = (-140 + 164) / 8 or x = (-140 - 164) / 8
x = 24 / 8 or x = -304 / 8
x = 3 or x = -38
Since the width of the deck cannot be negative, the width of the deck around the pool is 3 feet.