For the answer to this question,
Let x = depth of the gutter
then
18 - 2x = width of the gutter
Cross section area
A = depth x width
= x(18 - 2x)
A = 18x - 2x^2
:
Axis of symmetry will give x value for max area:
x = -b/(2a)
x = -18/(2x(-2))
x = 4.5 inches is the depth for max area
Max area: 4.5 * 9 = 40.5 sq/in
I hope my answer helped you.
