Question

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

6 cm

8 cm

5 cm

Answer 1

To determine which of the given choices cannot be the measure of the third side, we can use 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.

Let's check each choice:
- 10 cm: The sum of the two given sides (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.
- 6 cm: The sum of the two given sides (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 the two given sides (4 cm and 9 cm) is 13 cm, which is greater than 8 cm. Therefore, 8 cm can be the measure of the third side.
- 5 cm: The sum of the two given sides (4 cm and 9 cm) is 13 cm, which is not greater than 5 cm. Therefore, 5 cm cannot be the measure of the third side.

Therefore, the correct answer is 5 cm.