Question 379912: The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The dimensions of Eric’s pool are 9 feet by 7 feet.
He wants to build a walkway surrounding the pool so that the square footage
of the walkway and pool is 143 square feet.
How wide is one side of the walkway?
:
Let x = the width of the pool
Since the walkway goes all the way around the pool the over dimensions will be:
(2x+9) by (2x+7); then the overall area (pool & walkway) will be:
(2x+9)*(2x+7) = 143
FOIL
4x^2 + 14x + 18x + 63 = 143
:
4x^2 + 32x + 63 - 143 = 0
:
4x^2 + 32x - 80 = 0; our old friend, the quadratic equation!
Simplify, divide by 4
x^2 + 8x - 20 = 0
Factors to
(x+10)(x-2) = 0
The positive solution is what we want here
x = 2 ft is the width of the walkway
:
:
Check this solution by finding the area with the overall dimensions:
(4+7) * (4+9) =
11 * 13 = 143, confirms our solution of x=2
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