The 6 segments of the window frame shown in the diagram
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 that is 1 m wide and 3 m high. . . . . not needed
Determine the dimensions that will maximize the area of the window.
The total length of the framework is .
x / \ x
A * - - - * C
| x |
y | | y
* - - - *
The area of an equilateral triangle of side is: .
The area of the rectangle is: .
The total area is: .
Substitute  into : .
. . and that is the function you must maxiimize.