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.(1 point)
Responses
10 cm
5 cm
6 cm
8 cm
To determine which of the following choices cannot be the measure of the third side of the triangle, we will apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the two sides of the triangle measure 4 cm and 9 cm, we can evaluate each response to check if it satisfies the triangle inequality theorem.
- 10 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 10 cm. Therefore, 10 cm can be the measure of the third side.
- 5 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 5 cm. Therefore, 5 cm can be the measure of the third side.
- 6 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 6 cm. Therefore, 6 cm can be the measure of the third side.
- 8 cm: The sum of 4 cm and 9 cm is 13 cm, which is NOT greater than 8 cm. Therefore, 8 cm CANNOT be the measure of the third side.
Therefore, the measure of the third side cannot be 8 cm.