A long piece of galvanized sheet metal with width w is to be bent into a symmetric

Question:

A long piece of galvanized sheet metal with width w is to be bent into a symmetric form with three straight sides to make a rain gutter. A cross-section is shown in the figure.

(a) Determine the dimensions that allow the maximum possible flow; that is, find the dimensions that give the maximum possible cross-sectional area.
(b) Would it be better to bend the metal into a gutter with a semicircular cross-section?

х х w — 2х