Discussion

Find the length of the longest pole that can be placed in a room 12 m long, 8m broad and 9 m high.

Answer: B

The longest pole runs along the space diagonal of the room.

\[ d = \sqrt{l^{2} + b^{2} + h^{2}} \]

\[ = \sqrt{12^{2} + 8^{2} + 9^{2}} = \sqrt{144 + 64 + 81} = \sqrt{289} \]

\[ = 17 \text{ m} \]

The floor diagonal alone would be \( \sqrt{144 + 64} = 14.4 \) m; the height adds the third term.

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