Two sides of a triangle measure 4 cm and 9cm . Determine which of the following choices cannot be the measure of the third side .
8 cm
I0 cm
5 cm
6 cm
To determine which choice cannot be the measure of the third side, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, let the two sides of the triangle measure 4 cm and 9 cm.
For choice 8 cm: 4 cm + 8 cm = 12 cm > 9 cm, so this choice is possible.
For choice 10 cm: 4 cm + 10 cm = 14 cm > 9 cm, so this choice is possible.
For choice 5 cm: 4 cm + 5 cm = 9 cm, which is equal to the third side, so this choice cannot be the measure of the third side.
For choice 6 cm: 4 cm + 6 cm = 10 cm > 9 cm, so this choice is possible.
Therefore, the measure of the third side cannot be 5 cm.