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 458139: 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.
:
Assume the cross section of the gutter looks like this, horizontal portion is the width(w)
:
d|__|d
:
2d + w = 18
w = (18-2d)
and
the area
d * w = 28
Replace w with (18-2d)
d(18-2d) = 28
-2d^2 + 18d - 28 = 0
A quadratic equation, simplify, divide by -2, which also changes the signs
d^2 - 9d + 14 = 0
Factors to
(d-2)(d-7) = 0
Two solutions
d = 2 inches, then the width = 18-2(2) = 14 inches is the width
d = 7 inches, then the width = 18-2(7) = 4 inches is the width
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