SOLUTION: A rectangular swimming pool is twice as long as it is wide. A small sidewalk surrounds the pool. The walkway is a constant 2ft wide and has an area of 196 square feet. Find the dim

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Question 864642: A rectangular swimming pool is twice as long as it is wide. A small sidewalk surrounds the pool. The walkway is a constant 2ft wide and has an area of 196 square feet. Find the dimensions of the pool.

Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Pool length, x.
Pool width, y.
2 = width of walkway.
x=2y; so let us say:
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2y = pool length, and y = pool width
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Total Area combined walkway and pool is %282y%2B2%2A2%29%28y%2B2%2A2%29.
Pool Area is 2y%5E2.
Walkway area is given, 196 square feet.
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Those three parts give you Total=Pool%2BWalkway:
highlight_green%28%282y%2B4%29%28y%2B4%29=2y%5E2%2B196%29. This will be a quadratic equation. Can you do the rest?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can call the width of the pool +w+%7D%7D+and%0D%0Athe+length+%7B%7B%7B+2w+
The walkway adds +2+ ft to each side, so
+%28+w+%2B+2+%2B+2+%29%2A%28+2w+%2B+2+%2B+2+%29+=+w%2A2w+%2B+196+
+%28+w+%2B+4+%29%2A%28+2w+%2B+4+%29+=+2w%5E2+%2B+196+
+2w%5E2+%2B+8w+%2B+4w+%2B+16+=+2w%5E2+%2B+196+
+12w+%2B+16+=+196+
+12w+=+180+
+w+=+15+
+2w+=+30+
The dimensions of the pool are 15 ft x 30 ft
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check:
+%28+w+%2B+2+%2B+2+%29%2A%28+2w+%2B+2+%2B+2+%29+=+w%2A2w+%2B+196+
+%28+15+%2B+2+%2B+2+%29%2A%28+30+%2B+2+%2B+2+%29+=+450+%2B+196+
+19%2A34+=+646+
+646+=+646+
OK