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 5 cm 5 cm 8 cm 8 cm 10 cm 10 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 this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
The two given sides have lengths of 4 cm and 9 cm. So, we need to check if the sum of any of these lengths with the length of the third side is less than or equal to the length of the other side.
Let's check each choice:
- 6 cm: 4 + 6 = 10 > 9 and 6 + 9 = 15 > 4, so this is a possible length.
- 5 cm: 4 + 5 = 9 ≤ 9, so this is NOT a possible length.
- 8 cm: 4 + 8 = 12 > 9 and 8 + 9 = 17 > 4, so this is a possible length.
- 10 cm: 4 + 10 = 14 > 9 and 9 + 10 = 19 > 4, so this is a possible length.
The only choice that is NOT a possible length for the third side is 5 cm.
Therefore, the answer is 5 cm.