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)
5 cm
8 cm
6 cm
10 cm
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
For this triangle with sides measuring 4 cm and 9 cm, the sum of the two sides is 4 + 9 = 13 cm.
Now, let's check each of the possible third side lengths:
- 5 cm: 4 + 5 = 9, which is less than 9. This means that 5 cm can be the measure of the third side.
- 8 cm: 4 + 8 = 12, which is less than 9. This means that 8 cm can be the measure of the third side.
- 6 cm: 4 + 6 = 10, which is less than 9. This means that 6 cm can be the measure of the third side.
- 10 cm: 4 + 10 = 14, which is greater than 9. Therefore, 10 cm cannot be the measure of the third side.
Therefore, out of the given choices, 10 cm cannot be the measure of the third side of the triangle.