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)Responses6 cm6 cm8 cm8 cm10 cm10 cm5 cm
To determine which of the given choices cannot be the measure of the third side, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this to the given choices:
1) 6 cm: Since 4 cm + 6 cm = 10 cm which is greater than the other side of 9 cm, this could be the measure of the third side.
2) 8 cm: Since 4 cm + 8 cm = 12 cm which is greater than the other side of 9 cm, this could be the measure of the third side.
3) 10 cm: Since 4 cm + 10 cm = 14 cm which is greater than the other side of 9 cm, this could be the measure of the third side.
4) 5 cm: Since 4 cm + 5 cm = 9 cm, this is not greater than the other side of 9 cm. Therefore, 5 cm cannot be the measure of the third side.
Therefore, the answer is 5 cm.