---
id: 5900f3f61000cf542c50ff09
challengeType: 5
title: 'Problem 138: Special isosceles triangles'
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler138()</code> should return 1118049290473932.
    testString: assert.strictEqual(euler138(), 1118049290473932, '<code>euler138()</code> should return 1118049290473932.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler138() {
  // Good luck!
  return true;
}

euler138();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>