SOLUTION: A 23-ft by 47-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 296^2, how wide is the walkway?

Question 898236: A 23-ft by 47-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 296^2, how wide is the walkway?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A 23-ft by 47-ft rectangular swimming pool is surrounded by a walkway of uniform width.
If the total area of the walkway is 296^2, how wide is the walkway?
:
let x = width of the walkway
then the overall dimensions of the pool and the walkway:
(2x+23) by (2x+47)
:
Over-all area - pool area = walkway area (given as 296 cu/ft)
(2x+23)(2x+47) - (23*47) = 296
4x^2 + 94x + 46x + 1081 - 1081 = 296
Combine like terms to form a quadratic equation
4x^2 + 140x - 296 = 0
Simplify, divide by 4
x^2 + 35x - 74 = 0
factors to
(x+37)(x-2) = 0
the positive solution is the only reasonable solution
x = 2 ft is the width of the walkway
:
:
Check this
(27*51) - (23*47) =
1377 - 1081 = 296

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