SOLUTION: A Walkway of uniform width has area 72m ^2 and surrrounds a swimming pool that is 8m by 10m. Find the Width of the walkway

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Question 271540: A Walkway of uniform width has area 72m ^2 and surrrounds a swimming pool that is 8m by 10m. Find the Width of the walkway
Found 2 solutions by renhok, Alan3354:
Answer by renhok(1) About Me  (Show Source):
Answer by Alan3354(69443) About Me  (Show Source):
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A Walkway of uniform width has area 72m ^2 and surrrounds a swimming pool that is 8m by 10m. Find the Width of the walkway
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(w+8)*(w+10) = 72 + 80
w^2 + 18w + 80 = 152
w^2 + 18w - 72 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B18x%2B-72+=+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=%2818%29%5E2-4%2A1%2A-72=612.

Discriminant d=612 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+612+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+612+%29%29%2F2%5C1+=+3.36931687685298
x%5B2%5D+=+%28-%2818%29-sqrt%28+612+%29%29%2F2%5C1+=+-21.369316876853

Quadratic expression 1x%5E2%2B18x%2B-72 can be factored:
1x%5E2%2B18x%2B-72+=+%28x-3.36931687685298%29%2A%28x--21.369316876853%29
Again, the answer is: 3.36931687685298, -21.369316876853. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B-72+%29

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w = -9 + 3*sqrt(17) meters
w =~ 3.369 meters