SOLUTION: A rectangular pool is 50% longer than it is wide. It is surrounded by a path 1m wide. If the area of the path is 44 square metres, then find the area of the pool in square metres.

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Question 1037144: A rectangular pool is 50% longer than it is wide. It is surrounded by a path 1m wide. If the area of the path is 44 square metres, then find the area of the pool in square metres.
How? thanks.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
w width
L length
L=(3/2)w for 50% greater

Area of just the pool, top surface: wL
Area of combined pool and path: %28w%2B2%2A1%29%28L%2B2%2A1%29
JUST the path area around pool: %28w%2B2%29%28L%2B2%29-wL=44


Working with the path area equation may be easiest to start the algebra steps.
wL%2B2L%2B2w%2B4-wL=44
2L%2B2w%2B4-44=0
L%2Bw%2B2-22=0
L%2Bw-20=0
Now is a good place to substitute for L.
%283%2F2%29w%2Bw-20=0
3w%2B2w-40=0
5w-40=0
w-8=0
highlight%28w=8%29-------------highlight%28L=12%29


Pool top surface area is 96 square meters.