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 5 cm 8 cm 10 cm 6 cm

Answer 1

To determine the range of possible values for the third side of the triangle, 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.

Given that the two sides of the triangle measure 4 cm and 9 cm, the sum of these two sides is 4 + 9 = 13 cm. Therefore, the third side must be less than 13 cm in order for it to form a triangle.

Now, let's check each option to see if it falls within the valid range:

1. 5 cm: This is less than 13 cm, so it is a possible measure for the third side.
2. 8 cm: This is less than 13 cm, so it is a possible measure for the third side.
3. 10 cm: This is greater than 13 cm, so it cannot be the measure of the third side.
4. 6 cm: This is less than 13 cm, so it is a possible measure for the third side.

Therefore, the measure of 10 cm cannot be the measure of the third side of the triangle.