A window of perimeter (including the base of the arch) is in the form of a rectangle surrounded by a

Question

A window of perimeter (including the base of the arch) is in the form of a rectangle surrounded by a semi-circle. The semi-circular portion is fitted with coloured glass while the rectangular part is fitted with clear glass. The clear glass transmits three times as much light per square meter as the coloured glass does. What is the ratio for the sides of the rectangle so that the window transmits the maximum light?

Professor PC Thomas Classes · Answer

$\pi+6: 6$\