SOLUTION: A rectangular swimming pool, 20 meters long and 12 meters wide is surrounded by a deck that is the same with all around the pool.If the pool and deck together occupy an area of 600

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Question 958687: A rectangular swimming pool, 20 meters long and 12 meters wide is surrounded by a deck that is the same with all around the pool.If the pool and deck together occupy an area of 600 square meters, how wide is the deck?

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x=2 times the width of deck
%2820m%2Bx%29%2812m%2Bx%29=600m%5E2
x%5E2%2B32x%2B240=600m%5E2 Subtract 600m^2 from each side.
x%5E2%2B32x-360=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B32x%2B-360+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2832%29%5E2-4%2A1%2A-360=2464.

Discriminant d=2464 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+2464+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+2464+%29%29%2F2%5C1+=+8.81934729198171
x%5B2%5D+=+%28-%2832%29-sqrt%28+2464+%29%29%2F2%5C1+=+-40.8193472919817

Quadratic expression 1x%5E2%2B32x%2B-360 can be factored:
1x%5E2%2B32x%2B-360+=+1%28x-8.81934729198171%29%2A%28x--40.8193472919817%29
Again, the answer is: 8.81934729198171, -40.8193472919817. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B32%2Ax%2B-360+%29

x=8.82 meters, width=0.5x=4.41 meters
ANSWER The width of the deck is 4.41 meters.