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

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=47716 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 6.55499038637443, -48.0549903863744. Here's your graph:

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w = ~6.55 feet

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