Find Dimensions of the Pool

greatwhiteshark

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May 8, 2005
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A rectangular swimming pool is twice as long as it is wide. A small concrete walkway surrounds the pool. The walkway is a constant 2 feet wide and has an area of 196 square feet. Find the dimensions of the pool.

I got length = 60 feet and width = 30 feet. Am I right?

If not, can someone set up the proper equation that will help me find the dimensions on my own?
 
Hello, greatwhiteshark!

]A rectangular swimming pool is twice as long as it is wide.
A small concrete walkway surrounds the pool.
The walkway is a constant 2 feet wide and has an area of 196 square feet.
Find the dimensions of the pool.
Code:
     2     2x     2
   *----------------*
 2 |   :        :   |
   |...*--------*...|
   |   |        |   |
 x |   |       x|   |x+4
   |   |   2x   |   |
   |...*--------*...|
 2 |   :        :   |
   *----------------*
          2x+4
The dimensions of the pool are: x by 2x.
. . . Its area is: . (x)(2x) = 2x<sup>2</sup>

The large rectangle has area: .(2x + 4)(x + 4) .= .2x<sup>2</sup> + 12x + 16

The area of the walkway is the difference of these two areas:
. . . A .= .(2x<sup>2</sup> + 12x + 16) - 2x<sup>2</sup> .= .12x + 16

But we're told that the area of the walkway is 196 square feet.

So we have: . 12x + 16 . = . 196
. . . . . . . . . . . . . . . 12x . = . 180
. . . . . . . . . . . . . . . . . x . = . 15

Therefore, the pool is 15 feet by 30 feet.
 
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