---
id: 5900f3f71000cf542c50ff0a
title: 'Problem 139: Pythagorean tiles'
challengeType: 5
forumTopicId: 301767
dashedName: problem-139-pythagorean-tiles
---

# --description--

Let (a, b, c) represent the three sides of a right angle triangle with integral length sides. It is possible to place four such triangles together to form a square with length c.

For example, (3, 4, 5) triangles can be placed together to form a 5 by 5 square with a 1 by 1 hole in the middle and it can be seen that the 5 by 5 square can be tiled with twenty-five 1 by 1 squares.

However, if (5, 12, 13) triangles were used then the hole would measure 7 by 7 and these could not be used to tile the 13 by 13 square. Given that the perimeter of the right triangle is less than one-hundred million, how many Pythagorean triangles would allow such a tiling to take place?

# --hints--

`euler139()` should return 10057761.

```js
assert.strictEqual(euler139(), 10057761);
```

# --seed--

## --seed-contents--

```js
function euler139() {

  return true;
}

euler139();
```

# --solutions--

```js
// solution required
```
