Question 93161This question is from textbook
: problem, a garden area is 30ft long and 20ft wide. a path of uniform width is set around the edge. If the reamianing garden area is 400 ft^2, what is the width of the path. I know the total sq ft is 600 and the remaining is 200 sq ft but not sure how to go about getting answer. We have been working on the quadratic formula this week so i'm sure I am to solve the problem in that form, but now sure how, can someone help, Thanks
This question is from textbook
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! This same problem came up recently, this is what I submitted then, perhaps it will help you.
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A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
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Draw diagram of this; label the outside dimensions of the rectangle 30 by 20.
Label the width of the path as x, it will be apparent that the dimensions of
the garden (inside the path), will be (30-2x) by (20-2x)
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The area of the garden is given as 400 sq/ft
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A simple area equation:
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length times width = 400 sq/ft
(30-2x) * (20-2x) = 400
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FOIL:
600 - 60x - 40x + 4x^2 = 400
4x^2 - 100x + 600 = 400
4x^2 - 100x + 600 - 400 = 0
4x^2 - 100x + 200 = 0; a quadratic equation
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Simplify, divide by 4 and you have:
x^2 - 25x + 50 = 0
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We need to use the quadratic formula to solve this: a=1; b=-25;; c=50
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:
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Two solutions:
x = 22.8, not a possible solution, obviously
and
x = 2.19 ft is the width of the path
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Check our solution by finding the area of the garden
We have to subtract 2x from the outside dimensions: 2*2.19 = 4.38
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(30-4.38) * (20-4.38) =
25.62 * 15.62 = 400.2 ~ 400 sq/ft
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How about this, did it make sense to you, any questions?
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