Question 248947
If this isn't a calculus problem then we need to use the fact that a square maximizes the area for a rectangle with a given perimeter. Let's say the half circle at the top is R. Then each side of the square is 2*R. 

The perimeter of the semi-circle is half the circumference so that is 1/2(2*pi*R) which is then pi*R.

So the entire perimeter is given by:

pi*R + 3*(2*R)= 388.

Now you can solve for R.