a gothic window it to be built with 6 segments that total 6m in length. The window must fit inside an area that is 1m wide and 3 meters tall. the triangle on top must be equilateral. What is the maximum area of the window.
The Attempt at a Solution
so i made each of the sides of the trianle x and the width at the bottom of the rectangle x, then the sides of the rectangle equal to y. so the perimeter is 6=4x+2y
and the area A=1/2xh + xy
the height of the triangle would be 3-y wouldnt it? because then i plugged that in for h, and then isolated for y in the perimeter equation and plugged in y where it was necessary but i didnt get the right answer in the end after i got the derivative