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

## Description
<section id='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).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler390()</code> should return 2919133642971.
    testString: assert.strictEqual(euler390(), 2919133642971);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler390() {

  return true;
}

euler390();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>