SOLUTION: A rectangular swimmimg pool is surrounded by a walk. The area of the pool is 323 square feet and the outside dimensions of the walk are 20 feet by 22 feet. How wide is the walk?

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Question 336457: A rectangular swimmimg pool is surrounded by a walk. The area of the pool is 323 square feet and the outside dimensions of the walk are 20 feet by 22 feet. How wide is the walk?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular swimming pool is surrounded by a walk.
The area of the pool is 323 square feet and the outside dimensions of the walk
are 20 feet by 22 feet.
How wide is the walk?
:
let x = the width of the walkway
then the dimensions of the pool will be: (20-2x) by(22-2x)
Area of the pool given as 323, therefore:
:
(20-2x) * (22-2x) = 323
FOIL
440 - 40x - 44x + 4x^2 = 323
Arrange as a quadratic equation
4x^2 - 84x + 440 - 323 = 0
4x^2 - 84x + 117 = 0
this will factor to:
(2x - 3)(2x - 39) = 0
Only one solution makes sense
2x = 3
x = 1.5 ft is the width of the walkway
:
:
Check solution by finding the area
A = (20-3)(22-3)
A = 19 * 17
A = 323 sq/ft confirms our solutions