data/problems/390.yml
---
:id: 390
:name: Triangles with non rational sides and integral area
:url: https://projecteuler.net/problem=390
:content: |+
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+b<sup>2</sup>), √(1+c<sup>2</sup>) and √(b<sup>2</sup>+c<sup>2</sup>) (for positive integers b and c ) that have an integral area not exceeding n.
The example triangle has b=2 and c=8.
S(10<sup>6</sup>)=18018206.
Find S(10<sup>10</sup>).