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?
:
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 = {{{(-20)/(2*-2)}}}
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