---
id: 5900f41c1000cf542c50ff2f
title: 'Problem 176: Right-angled triangles that share a cathetus'
challengeType: 1
forumTopicId: 301811
dashedName: problem-176-right-angled-triangles-that-share-a-cathetus
---

# --description--

The four right-angled triangles with sides (9,12,15), (12,16,20), (5,12,13) and (12,35,37) all have one of the shorter sides (catheti) equal to 12. It can be shown that no other integer sided right-angled triangle exists with one of the catheti equal to 12.

Find the smallest integer that can be the length of a cathetus of exactly 47547 different integer sided right-angled triangles.

# --hints--

`trianglesSharingCathetus()` should return `96818198400000`.

```js
assert.strictEqual(trianglesSharingCathetus(), 96818198400000);
```

# --seed--

## --seed-contents--

```js
function trianglesSharingCathetus() {

  return true;
}

trianglesSharingCathetus();
```

# --solutions--

```js
// solution required
```
