2018-09-30 22:01:58 +00:00
---
id: 5900f41c1000cf542c50ff2f
title: 'Problem 176: Right-angled triangles that share a cathetus'
2020-11-27 18:02:05 +00:00
challengeType: 5
2019-08-05 16:17:33 +00:00
forumTopicId: 301811
2021-01-13 02:31:00 +00:00
dashedName: problem-176-right-angled-triangles-that-share-a-cathetus
2018-09-30 22:01:58 +00:00
---
2020-11-27 18:02:05 +00:00
# --description--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
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.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
Find the smallest integer that can be the length of a cathetus of exactly 47547 different integer sided right-angled triangles.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
# --hints--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
`euler176()` should return 96818198400000.
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
```js
assert.strictEqual(euler176(), 96818198400000);
2018-09-30 22:01:58 +00:00
```
2020-11-27 18:02:05 +00:00
# --seed--
2018-09-30 22:01:58 +00:00
2020-11-27 18:02:05 +00:00
## --seed-contents--
2018-09-30 22:01:58 +00:00
```js
function euler176() {
2020-09-15 16:57:40 +00:00
2018-09-30 22:01:58 +00:00
return true;
}
euler176();
```
2020-11-27 18:02:05 +00:00
# --solutions--
2018-09-30 22:01:58 +00:00
```js
// solution required
```