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
8 cm
8 cm
6 cm
6 cm
10 cm
10 cm
5 cm
To determine which of the choices cannot be the measure of the third side of the triangle, we can use the triangle inequality theorem.
According to the triangle inequality 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 apply this theorem to each of the choices:
1) 4 cm + 9 cm > 8 cm
This is true, so 8 cm can be the measure of the third side.
2) 4 cm + 9 cm > 6 cm
This is true, so 6 cm can be the measure of the third side.
3) 4 cm + 9 cm > 10 cm
This is also true, so 10 cm can be the measure of the third side.
4) 4 cm + 9 cm > 5 cm
This is false since 4 cm + 9 cm = 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.