1. ## calc optimization problem

The 6 segment ofthewindow frame shown in the diagram are tobe constructed from a piece of window framing material 6 m in length. A carpenterwants 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.

sorry my bad i forgot to post the rest of the question and the diagram which is basically a triangle on top of the square like this
.................................................. .............................A
.................................................. .............................*....
.................................................. ......................B *.......* C
.................................................. ....................... *******
.................................................. ........................*.........*
.................................................. ........................*.........*
.................................................. ........................*******

Determine the dimensions that should be used for the 6 pieces so that the maximum amount of light will be admitted.Assume no waste material for corner cuts and so on.

2. Originally Posted by anna12345
The 6 segment ofthewindow frame shown in the diagram ...
diagram?

3. 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 . $4x + 2y \:=\:6 \quad\Rightarrow\quad y \:=\:3 - 2x\;\;{\color{blue}[1]}$

The area of an equilateral triangle of side $x$ is: . $\tfrac{\sqrt{3}}{4}x^2$
The area of the rectangle is: . $xy$

The total area is: . $A \;=\;\tfrac{\sqrt{3}}{4}x^2 + xy\;\;{\color{blue}[2]}$

Substitute [1] into [2]: . $A \;=\;\frac{\sqrt{3}}{4}x^2 + x(3-2x)$

. . and that is the function you must maxiimize.