Answer:
3 feet
Step-by-step 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.
