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 poi
The third side of a triangle must be greater than the difference of the other two sides and less than the sum of the other two sides.
In this case, the difference between the two given sides is 9 cm - 4 cm = 5 cm. Therefore, the third side must be greater than 5 cm.
Now, let's check the given choices:
- 5 cm: This is the difference between the two given sides, so it could be the third side.
- 7 cm: This is greater than the difference between the two given sides (5 cm), so it could also be the third side.
- 12 cm: This is greater than the sum of the two given sides (4 cm + 9 cm = 13 cm), so it cannot be the third side.
- 3 cm: This is less than the difference between the two given sides (5 cm), so it cannot be the third side.
Therefore, the measure of the third side cannot be 12 cm.