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Mathematics

Find the length of the longest rod that can be placed in a room measuring 12 m × 9 m × 8 m.

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Answer

The dimensions of room :

Length = 12 m

Breadth = 9 m

Height = 8 m

Calculating the Diagonal of room,

Diagonal=l2+b2+h2=122+92+82=144+81+64=289=17 m.\text{Diagonal} = \sqrt{l^2 + b^2 + h^2} \\[1em] = \sqrt{12^2 + 9^2 + 8^2} \\[1em] = \sqrt{144 + 81 + 64} \\[1em] = \sqrt{289} \\[1em] = 17 \text{ m}.

Length of the longest rod that can be placed in a room = Length of the diagonal of the room.

∴ Length of the rod = 17 m.

Hence, length of the rod = 17 m.

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