## Special isosceles triangles

### Problem 138

Published on Saturday, 20th January 2007, 11:00 am; Solved by 2893

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.