freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-390-triangles-with-non-rational-sides-and-integral-area.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4f21000cf542c510005	Problem 390: Triangles with non rational sides and integral area	5	302055	problem-390-triangles-with-non-rational-sides-and-integral-area

--description--

Consider the triangle with sides \sqrt{5}, \sqrt{65} and \sqrt{68}. It can be shown that this triangle has area 9.

S(n) is the sum of the areas of all triangles with sides \sqrt{1 + b^2}, \sqrt{1 + c^2} and \sqrt{b^2 + c^2} (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}^6) = 18\\,018\\,206.

Find S({10}^{10}).

--hints--

nonRationalSidesAndIntegralArea() should return 2919133642971.

assert.strictEqual(nonRationalSidesAndIntegralArea(), 2919133642971);

--seed--

--seed-contents--

function nonRationalSidesAndIntegralArea() {

  return true;
}

nonRationalSidesAndIntegralArea();

--solutions--

// solution required