SOLUTION: A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 1
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Question 199443: A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet? Can you help me with this one?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet? Can you help me with this one?
.
Let x = width of gravel path
then
"area of walk" = "area of walk and garden" - "area of garden"
192 = (15+2x)(11+2x) - (15)(11)
192 = (15+2x)(11+2x) - 165
357 = (15+2x)(11+2x)
357 = 165 + 30x + 22x + 4x^2
357 = 165 + 52x + 4x^2
357 = 4x^2 + 52x + 165
0 = 4x^2 + 52x - 192
0 = x^2 + 13x - 48
0 = (x+16)(x-3)
x = {-16, 3}
We can toss out the negative solution leaving:
x = 3 feet
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