SOLUTION: Suzanne has a rectangular garden which is 48 feet long and 35 feet wide. She has 1260 square foot of paving stones, and she wants to build a pathway around the border of the garden

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Question 1120680: Suzanne has a rectangular garden which is 48 feet long and 35 feet wide. She has 1260 square foot of paving stones, and she wants to build a pathway around the border of the garden. How wide will the pathway be?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Suzanne has a rectangular garden which is 48 feet long and 35 feet wide. She has 1260 square foot of paving stones, and she wants to build a pathway around the border of the garden. How wide will the pathway be?
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w = the width of the pathway.
--> a rectangle 48+2w by 35+2w
Area = (48+2w)*(35+2w) = 4w^2 + 166w + 1680 sq ft
The inner rectangle is 48*35 = 1680
--> Area of walkway = 4w^2 + 166w
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4w^2 + 166w = 1260
4w^2 + 166w - 1260 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B166x%2B-1260+=+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=%28166%29%5E2-4%2A4%2A-1260=47716.

Discriminant d=47716 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-166%2B-sqrt%28+47716+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28166%29%2Bsqrt%28+47716+%29%29%2F2%5C4+=+6.55499038637443
x%5B2%5D+=+%28-%28166%29-sqrt%28+47716+%29%29%2F2%5C4+=+-48.0549903863744

Quadratic expression 4x%5E2%2B166x%2B-1260 can be factored:
4x%5E2%2B166x%2B-1260+=+%28x-6.55499038637443%29%2A%28x--48.0549903863744%29
Again, the answer is: 6.55499038637443, -48.0549903863744. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B166%2Ax%2B-1260+%29

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w = ~6.55 feet