Question

You're given two side lengths of 6 centimeters and 9 centimeters. Which measurement can you use for the length of the third side to construct a valid triangle?

Answer 1

It would be 9 centimeters.

Answer 2

Let's give names to the all sides a=6 , b=9 and c=?
Third sides of an triangle is determined by the following double  inequality, in this case b>a => b-a < c < b+a => 9-6 < c < 9+6 =>
3 < c < 15 => c belongs to the interval (3,15), let's take c=4, if we check for example side b => a>c => a-c < b < a=c => 6-4 < 9 < 6+4 =>
2 < 9 < 10 , inequality is true.