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 of the following 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 sides of the triangle are 4 cm and 9 cm. Let's check each of the given choices:
1) 6 cm: 4 cm + 6 cm > 9 cm - This choice is valid.
2) 8 cm: 4 cm + 8 cm > 9 cm - This choice is valid.
3) 5 cm: 4 cm + 5 cm < 9 cm - This choice is invalid since 4 cm + 5 cm is not greater than 9 cm.
4) 10 cm: 4 cm + 10 cm > 9 cm - This choice is valid.
Therefore, the third side cannot measure 5 cm.