SOLUTION: A family plans to surround their pool with a patio of constant width. The pool has an area of 150 square feet. The dimensions of the pool with the patio will be 15 feet by 20 feet.

Question 38576: A family plans to surround their pool with a patio of constant width. The pool has an area of 150 square feet. The dimensions of the pool with the patio will be 15 feet by 20 feet. Find the dimensions of the pool.
Thanks for answering!:-)
Found 2 solutions by Paul, rapaljer:
Answer by Paul(988) (Show Source): You can put this solution on YOUR website!
Letting x be the width of the patio:
Equation:
150=(15-2x)(20-2x)

x=2.5
Hence, the unifrom width is 2.5ft.
Paul.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = width of the patio around the pool.
The dimensions of the patio will be 15 feet by 20 feet, which includes x feet of patio on each side. Therefore the dimensions of the pool will be
15 -2x by 20-2x. Since the area of the pool is 150 square feet, the equation is
Area = (15-2x)(20 - 2x) = 150
300 -70x + 4x^2 = 150

Subtract 150 from each side and write the expression in descending powers of x:
4x^2 - 70x + 150 = 0

Divide both sides of the equation by 2:
2x^2 -35x + 75 = 0

Factor:
(2x-5)(x-15) = 0

Set each factor =0, and solve:
2x-5 = 0
2x = 5
x= 5/2 = 2.5 feet

or x-15= 0
x= 15. This answer is too wide for the path, so it must be rejected.

Therefore, the width of the path is 2.5 feet. The dimensions of the pool are
15-2x = 15-5 = 10 feet
20-2x = 20 -5 = 15 feet

Check: Does the area of the pool equal 150 feet? 10 ft x 15 ft = 150 sq ft. It checks!!

R^2 at SCC
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