This was kind of tricky. I made a diagram.
By the included diagram: R=OB=OC; y=AD, h=AB
AB is the height of the triangle, y is the length of the side.
Look at triangle ABC.
Look at triangle AOC.
Using these, we can solve for x.
The area of a triangle is 1/2xh.
There, R is a constant and it is in terms of h. Now, differentiate:
Set to 0 and solve for h.