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)

Question

Responses

6 cm
6 cm

5 cm
5 cm

8 cm
8 cm

10 cm

Answer 1

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

For the given triangle, the two sides measure 4 cm and 9 cm.
The possible lengths for the third side would be between 9 - 4 < third side < 9 + 4.
Simplifying, this becomes 5 < third side < 13.

Among the given choices, the length of the third side cannot be 10 cm because it falls outside the range of 5 < third side < 13.

Therefore, the answer is 10 cm.