## Triangles with non rational sides and integral area

### Problem 390

Published on Saturday, 23rd June 2012, 08:00 pm; Solved by 376

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.

S(106)=18018206.

Find S(1010).