Two sides of a triangle measures 4 cm and 9 cm. Determine which of the following choices cannot be the measure of the third side.
A: 6cm
B: 10cm
C: 8cm
D: 5m
In order for a triangle to be possible, the sum of the lengths of any two sides must be greater than the length of the third side.
The two sides given in the problem measure 4 cm and 9 cm.
Checking each choice:
- A: 4 cm + 6 cm = 10 cm, which is greater than 6 cm. So, option A is possible.
- B: 4 cm + 10 cm = 14 cm, which is greater than 9 cm. So, option B is possible.
- C: 4 cm + 8 cm = 12 cm, which is greater than 8 cm. So, option C is possible.
- D: 4 cm + 5 m = 5004 cm, which is much greater than 9 cm. So, option D is not possible.
Therefore, the measure of the third side cannot be 5 m.
The answer is $\boxed{\text{(D)}}$.