Question 102304: 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 16 square inches, find the depth of the gutter. (there are two answers a smaller value and a larger value)The width is represented by w-2x and the depth is x
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 16 square inches, find the depth of the gutter. (there are two answers a smaller value and a larger value)The width is represented by w-2x and the depth is x
:
Assume the illustration:
|__|x; is the cross-sectional area of 16 sq in and the sides & bottom = 18"
:
x = sides dimension
y = bottom dimension
:
2x + y = 18
y = (18-2x)
:
Area:
x * y = 16
:
Substitute (18-2x) for y:
x*(18-2x) = 16
-2x^2 + 18x - 16 = 0; a quadratic equation
:
Simplify, divide equation by -2
x^2 - 9x + 8 = 0
:
Factors to:
(x - 8) * (x - 1) = 0
x = +8
and
x = +1
:
The gutter can be:
8" high and 2" wide
or
1" high and 16" wide
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