SOLUTION: rectangular pool is 3 times as long as wide,surrounded by deck 2.5m wide. find dimension of pool if area deck is 265m

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Question 164989: rectangular pool is 3 times as long as wide,surrounded by deck 2.5m wide. find dimension of pool if area deck is 265m
Answer by josmiceli(9817) About Me  (Show Source):
You can put this solution on YOUR website!
Call the width of the pool
x
The length of the pool will then be
3x
The area of the pool is
x%2A3x+=+3x%5E2
If the deck around the pool is 2.5 m wide, then
2%2A2.5+=+5m are added to the width of the pool and
2%2A2.5+=+5m are added to the length of the pool
The area of the pool + deck =
%28x+%2B+5%29%2A%283x+%2B+5%29+=+3x%5E2+%2B+20x+%2B+25
Since it is given that the area of the deck is
A%5Bd%5D+=+265m, The area of the pool is
A%5Bp%5D+=+3x%5E2+%2B+20x+%2B+25+-+265, but A%5Bp%5D+=+3x%5E2, so
3x%5E2+=+3x%5E2+%2B+20x+%2B+25+-+265
Subtract 3x%5E2 from both sides
20x+-+240+=+0
20x+=+240
x+=+12
3x+=+36
The pool is 12m x 36m
check answer:
x%2A3x+=+12%2A36
A%5Bp%5D+=+432
A%5Bd%5D+%2B+A%5Bp%5D+=+265+%2B+432
A%5Bd%5D+%2B+A%5Bp%5D+=+697, and, from above,
A%5Bd%5D+%2B+A%5Bp%5D+=+3x%5E2+%2B+20x+%2B+25
A%5Bd%5D+%2B+A%5Bp%5D+=+3%2A144+%2B+240+%2B+25
A%5Bd%5D+%2B+A%5Bp%5D+=+432+%2B+265
A%5Bd%5D+%2B+A%5Bp%5D+=+697
OK