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Question 410631: A swimming pool area has a 5-foot wide concrete path all around it. The width of the pool is half of the length. The area of the pool and path together is 1,000 square feet. What is the total area of the concrete path.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A swimming pool area has a 5-foot wide concrete path all around it.
The width of the pool is half of the length.
The area of the pool and path together is 1,000 square feet.
What is the total area of the concrete path.
:
Let L = length of the pool
Let W = width of the pool
:
A 5' walkway all the way around will add 10' to the length and width of the pool
Therefore
(L+10)*(W+10) = 1000 sq/ft
The length is twice as long as the width, therefore we can write it:
(2W+10)*(W+10) = 1000
FOIL
2W^2 + 20W + 10W + 100 = 1000
2W^2 + 20W + 10W + 100 - 1000 = 0
2W^2 + 30W - 900 = 0
simplify, divide by 2
W^2 + 15W - 450 = 0
This factors to
(W + 30)(W - 15) = 0
The positive solution:
W = 15 ft is the width of the pool
then
2(15) = 30 ft is the length
and
15 * 30 = 450 sq/ft is the area of the pool
:
Total area - pool area = concrete path area
1000 - 450 = 550 sq/ft is the concrete path area
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