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 6 cm 6 cm 8 cm 8 cm 5 cm 5 cm 10 cm.
To determine which choice cannot be the measure of the third side, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
For a triangle with sides measuring 4 cm, 9 cm, and x cm, the triangle inequality theorem gives us:
4 + x > 9
x > 5
9 + x > 4
x > -5 (since lengths cannot be negative)
So, we know that the length of the third side must be greater than 5 cm, but not negative.
Looking at the choices:
- 6 cm is greater than 5 cm, so it can be the measure of the third side.
- 8 cm is greater than 5 cm, so it can be the measure of the third side.
- 5 cm is equal to one of the given side lengths, so it cannot be the measure of the third side.
- 10 cm is greater than 5 cm, so it can be the measure of the third side.
Therefore, the choice that cannot be the measure of the third side is 5 cm.