Question 551394: 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? Please, thank you~ :)
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 748ft^2, determine the dimensions of the pool?
:
Let w = the width of the pool
It said,"The length of a rectangular swimming pool is twice its width." therefore
2w = the length of the pool
Area = length * width, therefore:
2w * w = 2w^2; the area of the pool
:
Surrounded by a 4' walk; the overall dimensions (pool & walkway):
(w+8) by (2w+8)
:
Overall area - pool area = walkway area (given as 748sq/ft)
(w+8)*(2w+8) - 2w^2 = 748
FOIL
2w^2 + 8w + 16w + 64 - 2w^2 = 748
combine like terms
2w^2 - 2w^2 + 24w = 748 - 64
A simple equation
24w = 684
w = 28.5 ft is the width of the pool
and
2(28.5) = 57 ft is the length of the pool
:
:
see if this checks out.
find the overall area, subtract the pool area should equal the walkway area
(57+8)(28.5+8) = 2372.5
. . . . 57*28.5 = 1624.5
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walkway area = 748
:
I tried to make this as understandable as possible, did I succeed? C
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