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Question 778633: I never received a confirmation email about my question so here it is again:
A particular rectangular swimming pool is twice as long as it is wide. There is a concrete walkway around the perimeter of the pool. The walkway is a constant 2 feet wide. The walkway has an area of 100 square feet. What are the dimensions of the pool?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A particular rectangular swimming pool is twice as long as it is wide.
There is a concrete walkway around the perimeter of the pool.
The walkway is a constant 2 feet wide.
The walkway has an area of 100 square feet.
What are the dimensions of the pool?
:
let L = the length of the pool
let w = the width
:
A 2 ft walkway adds 4 ft to the length & width giving us the overall dimensions
Overall area - pool area = 100 sq ft, (area of the walkway)
(L+4)(w+4) - L*W = 100
L = 2w, replace L with 2w
(2w+4)(w+4) = 2w*w = 100
FOIL
2w^2 + 8w + 4w + 16 - 2w^2 = 100
the 2w^2's cancel leaving us with
12w = 100 - 16
12w = 84
w = 84/12
w = 7 ft is the width of the pool
therefore
2(7) = 14 ft is the length of the pool
:
:
See if this checks out, find the overall area and the area of the pool
18*11 = 198
14*7 = 98
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diff: 100 sq/ft, the area of the walkway
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