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.(1 point)
Responses

10 cm
10 cm

8 cm
8 cm

6 cm
6 cm

5 cm

Answer 1

To determine which of the following choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem. According to this 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 consider the sides of the triangle given:
Side 1: 4 cm
Side 2: 9 cm

Now, let's check each of the choices:

1) 10 cm: 4 cm + 9 cm = 13 cm, which is greater than 10 cm. This can be the third side.

2) 8 cm: 4 cm + 9 cm = 13 cm, which is greater than 8 cm. This can be the third side.

3) 6 cm: 4 cm + 9 cm = 13 cm, which is greater than 6 cm. This can be the third side.

4) 5 cm: 4 cm + 9 cm = 13 cm, which is greater than 5 cm. This can be the third side.

Therefore, all of the choices, 10 cm, 8 cm, 6 cm, and 5 cm, can be the measure of the third side of the triangle. None of the choices cannot be the measure of the third side.