Explanation:

To find the length of the longest pole that can be placed in the room, we calculate the room's space diagonal using the formula:

$$ \text{Length of diagonal} = \sqrt{l^2 + w^2 + h^2} $$

- Given:

- Length (l) = 16 m

- Width (w) = 8 m

- Height (h) = 11 m

- Calculation:

- Diagonal = \(\sqrt{16^2 + 8^2 + 11^2}\)

- Diagonal = \(\sqrt{256 + 64 + 121}\)

- Diagonal = \(\sqrt{441}\)

- Diagonal = 21 m

- Interpretation of Options:

- Option 1: 20 m – too short

- Option 2: 21 m – Correct

- Option 3: 19 m – too short

- Option 4: 18 m – too short