Cross Sections and Area

Question

A rain gutter is made from sheets of aluminum that are 1212 inches wide by turning up the edges to form right angles. Determine the depth of the gutter that will maximize its cross- sectional area and allow the greatest amount of water to flow. What is the maximum cross-sectional area?

 

Even just the equation to solve it would be handy. I cant get to that part 

Answer 1

No doubt you have mis-typed the measurement; should be 12"

Let flat bottom of cross-section rectangle be 12-2x and each vertical side be x in length.
Area = x(12-2x) = p(x)
p'(x) = (12-2x) + x(-2), using product rule. Setting this to zero gives x=3. So width is 6", ht. = 3"