SOLUTION: An industrial rain gutter is constructed by folding the edges of a sheet of metal 20 inches wide so that the cross section of the gutter is a rectangle. How much edge should be f

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Question 583241: An industrial rain gutter is constructed by folding the edges of a sheet of metal
20 inches wide so that the cross section of the gutter is a rectangle. How much edge
should be folded up on each side to maximize the area of the cross section?
im the picture it shows that it has 3 divisions the 2 sides and the base

its problen two in this websiter
http://math.arizona.edu/~cjewell/112/homework/Homework13.pdf
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
An industrial rain gutter is constructed by folding the edges of a sheet of metal
20 inches wide so that the cross section of the gutter is a rectangle.
How much edge should be folded up on each side to maximize the area of the cross section?
:
End would look something like this |__|
Let the vertical sides = s
Let the horizontal = b
then
2s + b = 20 inches
b = (20-2s)
and
Area = s * b
replace b with (20-2s)
A = s(20-2s)
A = -2s^2 + 20s
This is a quadratic equation, we can find max area by finding the axis of symmetry. Formula: x = -b/(2a)
s =
s = +5 inches on each side will give the max area
:
Find the area
b = 20 - 2(5)
b = 10 is the base
A = 5 * 10
A = 50 sq/in is max area