Explanation:

To find the length of the longest pole that can be fitted in a room, we need to calculate the room's diagonal. This involves using the 3D Pythagorean theorem. Here’s the breakdown:

- Room dimensions: 12 m (length) x 6 m (width) x 4 m (height).

- Diagonal formula: \(\sqrt{(Length^2 + Width^2 + Height^2)}\).

- Calculation:

- \(\sqrt{(12^2 + 6^2 + 4^2)}\).

- \(\sqrt{(144 + 36 + 16)}\).

- \(\sqrt{196}\).

- The diagonal length is 14.0 m.

- Options considered:

- Option 1: 7.2 m - Too short.

- Option 2: 14.0 m - Correct calculation.

- Option 3: 13.4 m - Incorrect.

- Option 4: 12.6 m - Incorrect.