Question

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?

Answer 1

3 feet

Explanation:

Let x represent the width of the deck. The deck adds to the pool dimensions on both sides, so the area of the site including pool and deck will be ...

A = (20 +2x)(50 +2x) = 1000 +140x +4x^2

The area of the pool alone is

A = (20)(50) = 1000

So, the area of the deck is the difference:

456 = (4x^2 +140x +1000) -(1000)

Dividing by 4 and subtracting 114, we have ...

x^2 +35x -114 = 0

(x -3)(x +38) = 0

Solutions to this are x = 3 and x = -38. The positive solution is the one of interest.

The deck is 3 feet wide.