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Question 239265: RAIN-GUTTER DESIGN: An open rectangle gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross- section of the gutter is 50 in^2. Can you please help me find the depth.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! RAIN-GUTTER DESIGN: An open rectangle gutter is made by turning up the sides of a piece of metal 20 in. wide.
The area of the cross- section of the gutter is 50 in^2.
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Let d = the depth
Let w = the width of the gutter
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d|__|d would be a picture of the end of it, the horizontal line is the width (w)
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the piece of metal is 20" wide, therefore:
2d + w = 20
w = (20-2d)
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The area = depth * width
d * w = 50
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Replace w with (20-2d)
d(20-2d) = 50
-2d^2 + 20d - 50 = 0; our old friend, the quadratic equation!
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Simplify and change the signs, divide by -2
d^2 - 10d + 25 = 0
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Factors easily to:
(d - 5)(d - 5) = 0
d = 5 inches is the depth
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Lets see if this is true
w = 20 - 2d
w = 20 - 10
w = 10 inches is the width
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Check the area 5 * 10 = 50
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Did this make sense to you? Did I explain it well enough for you to understand?
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