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.
A. 5 cm
B. 8 cm
C. 6 cm
D. 10 cm
To determine which choice cannot be the measure of the third side, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider each choice:
A. 5 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 5 cm. Therefore, choice A could be the measure of the third side.
B. 8 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 8 cm. Therefore, choice B could be the measure of the third side.
C. 6 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is less than 6 cm. Therefore, choice C cannot be the measure of the third side.
D. 10 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is less than 10 cm. Therefore, choice D cannot be the measure of the third side.
Therefore, the answer is choice C.