---
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.

<img class="img-responsive center-block" alt="two 5 x 5 squares: one with four 3x4x5 triangles placed to create 1x1 hole in the middle; second with twenty-five 1x1 squares" src="https://cdn.freecodecamp.org/curriculum/project-euler/pythagorean-tiles.png" style="background-color: white; padding: 10px;">

However, if (5, 12, 13) triangles were used, the hole would measure 7 by 7. These 7 by 7 squares 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 occur?

# --hints--

`pythagoreanTiles()` should return `10057761`.

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

# --seed--

## --seed-contents--

```js
function pythagoreanTiles() {

  return true;
}

pythagoreanTiles();
```

# --solutions--

```js
// solution required
```