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

If we have a triangle with sides a, b, c then

b-a < c < b+a

describes the restriction of the length of side c, given sides a and b. This is due to the triangle inequality theorem.

a = 6

b = 9

b-a < c < b+a

9-6 < c < 9+6

3 < c < 15

Answer: The third side is between 3 cm and 15 cm. The third side cannot equal 3 cm, and it also cannot equal 15 cm.