According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle has to be greater than the length of the third side. Note that the only sum we must test is the smallest and middle side against the greatest side.
7+10? >20 ⇔ 17≯ 20 *
Since the sum of the smallest and middle side is less than the length of the longest side, we cannot draw such a triangle because the smallest and middle side will never meet.
