SOLUTION: A piece of sheet metal, w = 20 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 48 square inches, find the depth of the gutter.
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Question 942634: A piece of sheet metal, w = 20 inches wide, is bent to form the gutter shown in the illustration. If the cross-sectional area is 48 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 = 20 inches wide, is bent to form the gutter shown in the illustration.
If the cross-sectional area is 48 square inches, find the depth of the gutter.
:
let d = the debth of the gutter
let x =the width of the gutter
:
Sort of like this, the width is x
d|__|d
;
We know: 2d + x = 20
therefore:
x = (20-2d)
:
and
x*d = 48, the cross-sectional area
Replace x with (20-2d)
d(20-2d) = 48
A quadratic is equation is formed
-2d^2 + 20d - 48 = 0
Simplify, divide by -2
d^2 - 10d + 24
Factors to
(d-6)(d-4) = 0
Two solutions
d = 6
d = 4
Find x
when d = 6 inches
x = 20 - 2(6)
x = 8 inches wide (6*8=48 square inches)
:
when d = 4 inches
x = 20 - 2(4)
x = 12 inches wide (4*12=48 square inches)
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