From a strip of tin 14 inches a trapezoidal gutter is to be made by bending up the sides at an angle of 45°. Find the width of the base for greatest carrying capacity.

Answer 1

If the folded up edges have length x, then the base is 14-2x

The area is thus

a = ((14-2x + √2 x)+(14-2x))/2 * x/√2
da/dx = (1-2√2)x + 7√2
da/dx=0 when x = 4+√2
So, the base is 14-(4+√2) = 10-√2