optimization f(x,y, B)

[mammothrob]

so I have a isocolese triange surrmounted on a rectagle to create a window with a perimeter of 12.

So ive been trying to figure out how to find the demensions of x y and angle B that maximize the area. xy are the sides of the rectangle and B is the angle between the top of the rectangle side x and length of triangle.

I assume that the the max area of a triangle is if it is equateral. so the angle would have to be 60 assuming that I dont have give some of the triangles length to the rectangle. I then used [(x^2)sin60sin60]/sin(120) for the area formula. Ya.... so I computed partial derivative for x and y and wasnt able to get critical points. Im now lost... any hints? I have a feeling that chooseing 60 degrees was a bad assumption, but I could not think of another way to get a formula including the anlge that wouldnt give me 4 variables. any help appreciated.

Rob

 

[galactus]

If the triangle is isosceles, you can't assume theta is 60 degrees.

Is the entire window perimeter 12?.

If so, \(\displaystyle P=2x+y+2s=12\)

\(\displaystyle A=xy+\frac{\sqrt{3}}{4}s^{2}\)

Is this your window: