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?
2 feet
3 feet
4 feet
5 feet
4 feet
To find the width of the deck around the pool, we first need to calculate the total area of the pool and deck combined.
Total area = (width of pool + 2*width of deck)(length of pool + 2*width of deck)
Total area = (20 + 2x)(50 + 2x)
Total area = 1000 + 140x + 4x^2
Given that the total area of the pool and deck combined is 456 square feet, we can set up the following equation:
1000 + 140x + 4x^2 = 456
4x^2 + 140x - 544 = 0
Now we need to solve this quadratic equation to find the width of the deck around the pool:
Using the quadratic formula, we get:
x = (-140 ± √(140^2 - 4*4*(-544)))/(2*4)
x = (-140 ± √(19600 + 8704))/8
x = (-140 ± √28304)/8
x = (-140 ± 168)/8
Now we have two solutions for x: x = (-140 + 168)/8 = 28/8 = 3.5 and x = (-140 - 168)/8 = -308/8 = -38.5. However, since the width of the deck cannot be negative, the width of the deck around the pool is 3.5 or 4 feet. Since the deck must be the same width all the way around the pool, the width of the deck around the pool is 4 feet.