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.