What are the possible side lengths of a triangle

1. Consider a triangle with sides a, b and c.

2. a, b and c can be sides of a triangle only if each of these conditions hold:

         i)  a+b>c
         ii) b+c>a
and   iii)a+c>b

3. So the only condition for 3 numbers to be the side lengths of a triangle is that the sum of any 2 of them must be larger than the third number

4. This is called the "triangle inequality".