SOLUTION: The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748ft^2, determine the dimensions of the

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Question 151386: The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748ft^2, determine the dimensions of the pool?

Answer by ankor@dixie-net.com(22740) (Show Source):
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The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748ft^2, determine the dimensions of the pool.
:
Let x = width of the pool
then
2x = length of the pool
hence
Pool area = 2x^2
:
A 4' walkway will add 8' and the overall dimensions will be:
(x+8) by (2x+8)
Overall area:
(x+8)(2x+8) = 2x^2 + 24x + 64 sq/ft
:
Overall area - pool area = walkway area (given as 748 sq/ft)
:
(2x^2 + 24x + 64) - 2x^2 = 748
;
2x^2 - 2x^2 + 24x = 748 - 64
:
24x = 684
x =
x = 28.5 ft is the width of the pool
:
2(28.5) = 57 ft is the length of the pool
;
:
Check the solutions by finding the areas:
(36.5 * 65) - (28.5 * 57)
2372.5 - 1624.5 = 748; confirms our solution