yaworsw/euler-manager

---
:id: 138
:name: Special isosceles triangles
:url: https://projecteuler.net/problem=138
:content: |+
  Consider the isosceles triangle with base length, _b_ = 16, and legs, L = 17.

   ![]({{ images_dir }}/p138.gif)

  By using the Pythagorean theorem it can be seen that the height of the triangle, _h_ = √(17<sup>2</sup> − 8<sup>2</sup>) = 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.