The program should raise an error if the triangle cannot exist.

The triangle inequality theorem states: z ≤ x + y where x,y, and z are the lengths of the sides of a triangle. In other words, the sum of the lengths of any two sides of a triangle always exceeds or is equal to the length of the third side.

A corollary to the triangle inequality theorem is there are two classes of triangles--degenerate and non-degenerate. If the sum of the lengths of any two sides of a triangle is greater than the length of the third side, that triangle is two dimensional, has area, and belongs to the non-degenerate class. In mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class. The degenerate case of the triangle inequality theorem is when the sum of the lengths of any two sides of a triangle is equal to the length of the third side. A triangle with such qualities is qualitatively different from all the triangles in the non-degenerate class since it is one dimensional, looks like a straight line, and has no area. Such triangles are called degenerate triangles and they belong to the degenerate class.

This exercise does not test for degenerate triangles. Feel free to add your own tests to check for degenerate triangles.