Discussion
The length of the longest pole that can be placed in a hall of dimensions 10 m x 8 m x 6 m, is:
Answer: C
The longest pole is \(10\sqrt{2}\) m.
The longest straight pole in a box-shaped hall runs along the space diagonal, from one bottom corner to the opposite top corner:
\[ \begin{aligned} d &= \sqrt{10^{2} + 8^{2} + 6^{2}} \\ &= \sqrt{100 + 64 + 36} = \sqrt{200} \\ &= 10\sqrt{2} \approx 14.1\ \text{m} \end{aligned} \]
\(8\sqrt{2}\) m (about 11.3 m) and 11 m are shorter than this. 9 m is shorter even than the 10 m length of the floor, so it cannot be the longest pole.
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