The length and breadth of a room are 21 m and 16 m respectively. If the length of the longest rod that can be placed in the room is 29 m, then what is the height of the room?

Explanation

The longest rod corresponds to the body diagonal of the cuboidal room: d = \sqrt{l^2 + b^2 + h^2}. We have 29 = \sqrt{21^2 + 16^2 + h^2} \implies 841 = 441 + 256 + h^2 \implies 841 = 697 + h^2 \implies h^2 = 144 \implies h = 12\text{ m}.

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