Question 666646: 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 748 feet squared, determine the dimensions of the pool.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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 748 feet squared, determine the dimensions of the pool.
:
Let L = the length of the pool
Let W = the width
:
Overall dimensions including the cement walk, a 4' walk adds 8' to the dimensions
(L+8) by (W+8)
"The length is twice the width, therefore we can write the overall dimension:
(2w+8) by (w+8)
:
Overall area - pool area = walk area (748 sq/ft)
(2W+8)*(w+8) - 2w*w = 748
2w^2 + 16w + 8w + 64 - 2w^2 = 748
combine like terms
2w^2 - 2w^2 + 24w = 748 - 64
24w = 684
w = 684/24
w = 28.5 ft is the width of the pool
and
2(28.5) = 57 ft is the length of the pool
:
:
See if that checks out:; Overall dimensions will be 65 by 36.5:
(65*36.5) - (57*28.5) =
2372.5 - 1624.5 = 748; confirms our solution: pool is 57 by 28.5 ft
:
Hey, did this make sense to you? C
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