Final answer:
The length of the third side of the triangle must be greater than 3 cm and less than 15 cm, according to the Triangle Inequality Theorem.
Step-by-step explanation:
To determine the possible lengths of the third side of a triangle with sides of 9 cm and 6 cm, we can use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Thus, the length of the third side must be more than the difference (9 cm - 6 cm = 3 cm) and less than the sum (9 cm + 6 cm = 15 cm) of the other two sides. Therefore, the length of the third side can be any value greater than 3 cm and less than 15 cm, without including these numbers.