Two sides of a triangle measure 4 cm and 9 cm. What is the greatest integer number of centimeters that could be the third side of this triangle?
To solve this problem, I need to recall the triangle inequality theorem, which says that the sum of any two sides of a triangle must be greater than the third side. This means that the third side of the triangle must be less than 4 + 9 = 13 cm. The greatest integer number of centimeters that is less than 13 is 12. Therefore, the answer is 12 cm.

