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

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14m

16m

15m

17m

answer is D.

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Detailed Solution

Given, the dimensions of the room are,
Length = 12m,
Breadth = 9m,
Height = 8m.
The length of the longest diagonal of a cuboid = length of longest rod
Length of diagonal of a cuboid is given by

L d i a g o n a l = l 2 + b 2 + h 2

L = 122 + 92 + 82

L = 144 + 81 + 64

L = 289

L = 17

m
Thus, the length of the longest rod is 17m.
Therefore, the correct option is 4.

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