---
id: 5900f3f61000cf542c50ff09
title: 'Problem 138: Special isosceles triangles'
challengeType: 5
forumTopicId: 301766
dashedName: problem-138-special-isosceles-triangles
---

# --description--

Consider the isosceles triangle with base length, b = 16, and legs, L = 17.

By using the Pythagorean theorem it can be seen that the height of the triangle, h = √(172 − 82) = 15, which is one less than the base length. With b = 272 and L = 305, we get h = 273, which is one more than the base length, and this is the second smallest isosceles triangle with the property that h = b ± 1. Find ∑ L for the twelve smallest isosceles triangles for which h = b ± 1 and b, L are positive integers.

# --hints--

`euler138()` should return 1118049290473932.

```js
assert.strictEqual(euler138(), 1118049290473932);
```

# --seed--

## --seed-contents--

```js
function euler138() {

  return true;
}

euler138();
```

# --solutions--

```js
// solution required
```