two sides of a triangle measure 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.
5
6
10
8
To determine which of the choices cannot be the measure of the third side, we need to 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.
In this case, we have two sides measuring 4 cm and 9 cm. Let's check each of the given choices to see if they satisfy the triangle inequality theorem:
Choice 5: 4 + 5 = 9, which is equal to the third side of 9 cm. This choice is valid.
Choice 6: 4 + 6 = 10, which is less than the third side of 9 cm. This choice is not valid.
Choice 10: 4 + 10 = 14, which is greater than the third side of 9 cm. This choice is valid.
Choice 8: 4 + 8 = 12, which is greater than the third side of 9 cm. This choice is valid.
Therefore, the measure of the third side cannot be 6 cm.