Hello, Anna!

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. Code:

B
*
/ \
x / \ x
/ \
A * - - - * C
| x |
y | | y
| |
* - - - *
x

The total length of the framework is .

The area of an equilateral triangle of side is: .

The area of the rectangle is: .

The total area is: .

Substitute [1] into [2]: .

. . and *that* is the function you must maxiimize.