The six segments of the window frame (which is an equilateral triangle on top of a rectangle) are to be constructed from a piece of window framing material 6 m in length. A carpenter wants to build a frame for a rural gothic style window where triangle ABC is equilateral. The window must fit inside a space 1 m wide and 3 m wide.
Determine the dimensions that should used for the six pieces so that the maximum amount of light will be admitted. Assume no waste material for corner cuts and so on.