I would try to write the perimeter and the area as functions of x and r. Question: is the rectangle really a square? You don't provide another dimension for it, so I'm kind of assuming you have a square.
a norman window is a semi-circle sermounted on top of a rectangle. assum Parimeter of the window is P, a constant. Show the area of window is maximum when both x and r are equal to P/pi+4.
Show maximum area is 1/2p^2/pi+4
Stuck I tried solving for P first bu I think it is incorrect.
No, I don't think you have it yet. The perimeter is one-half of a circle (the semicircle part), plus three sides of the rectangle (don't count the border between the rectangle and the semi-circle).
For the area, you've only computed the area of the semicircle. What's the area of the rectangle? That has to be added into your formula as well.
So, what do you get?