2 sides of a triangle measure 4 cm and 9 cm. determine which of the following choices cannot be the measure of the third side.
To determine the possible range of the third side's length, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that two sides of the triangle measure 4 cm and 9 cm, the third side must be greater than the difference between the two sides (9 - 4 = 5) and less than the sum of the two sides (9 + 4 = 13).
So, the third side length cannot be:
- 7 cm: This is within the possible range (5 < 7 < 13)
- 8 cm: This is within the possible range (5 < 8 < 13)
- 10 cm: This is within the possible range (5 < 10 < 13)
- 12 cm: This is within the possible range (5 < 12 < 13)
- 14 cm: This is outside the possible range (5 < 14)
Therefore, the third side length cannot be 14 cm.