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

# --description--

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).

# --hints--

`euler390()` should return 2919133642971.

```js
assert.strictEqual(euler390(), 2919133642971);
```

# --seed--

## --seed-contents--

```js
function euler390() {

  return true;
}

euler390();
```

# --solutions--

```js
// solution required
```