Problem 138

Special isosceles triangles

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* = (17^{2} 8^{2}) = 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.

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