SOLUTION: A piece of sheet metal, w = 18 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 28 square inches, find the depth of the gutter.
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Question 400594: A piece of sheet metal, w = 18 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 28 square inches, find the depth of the gutter.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A piece of sheet metal, w = 18 inches wide, is bent to form the gutter shown in the illustration.
If the cross-sectional area is 28 square inches, find the depth of the gutter.
:
Let d = the debth of the gutter
then
(18-2d) = the width of the gutter
:
d|__|d
The bottom dimension is (18-2d)
:
The cross sectional area:
d(18-2d) = 28
-2d^2 + 18d = 28
A quadratic equation
-2d^2 + 18d - 28 = 0
Multiply by -1, to make it easier to factor
2d^2 - 18d + 28 = 0
Factors to
(2d - 4)(d - 7) =
Two solutions
2d = 4
d = 2
and
d = 7 inches is probably the reasonable value for the depth of gutter
:
:
Check:
the width of the gutter 18 - 2(7) = 4 inches
Check the area: 7 * 4 = 28 sq/inches
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