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.
10 cm
5 cm
6 cm
8 cm
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, the two sides of the triangle measure 4 cm and 9 cm.
Let's test each of the choices to see if it satisfies the triangle inequality:
1. 10 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 10 cm. So, 10 cm can be the measure of the third side.
2. 5 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 5 cm. So, 5 cm can be the measure of the third side.
3. 6 cm: The sum of 4 cm and 9 cm is 13 cm, which is greater than 6 cm. So, 6 cm can be the measure of the third side.
4. 8 cm: The sum of 4 cm and 9 cm is 13 cm, which is not greater than 8 cm. So, 8 cm cannot be the measure of the third side.
Therefore, the answer is 8 cm.