Triangles with non rational sides and integral area
Consider the triangle with sides √5, √65 and √68. It can be shown that this triangle has area 9.
S(n) is the sum of the areas of all triangles with sides √(1+b2), √(1+c2) and √(b2+c2) (for positive integers b and c ) that have an integral area not exceeding n.
The example triangle has b=2 and c=8.