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.

Question

A: 8 cm

B:10 cm

C: 5 cm

D: 6 cm

Answer 1

C: 5 cm cannot be the measure of the third side.

To see why, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

In this case, the two given sides are 4 cm and 9 cm. So we need to check if the sum of these sides is greater than each of the answer choices.

- For choice A, 8 cm, the sum of 4 cm and 8 cm is 12 cm, which is greater than the third side.
- For choice B, 10 cm, the sum of 4 cm and 10 cm is 14 cm, which is greater than the third side.
- For choice D, 6 cm, the sum of 4 cm and 6 cm is 10 cm, which is greater than the third side.

However, for choice C, 5 cm, the sum of 4 cm and 5 cm is only 9 cm, which is not greater than the third side. Therefore, C cannot be the measure of the third side.

Answer 2

what a lot of words! Just recall that
9-4 < x < 9+4
5 < x < 13
so C:5 is not possible