Question : What is the length (in metres) of the longest rod that can be placed in a room which is 2 metre long, 2 metre broad, and 6 metre high?
Option 1: $8$
Option 2: $2\sqrt{11}$
Option 3: $3\sqrt{11}$
Option 4: $10$
Correct Answer: $2\sqrt{11}$
Solution :
Longest rod that can be placed in a room
= diagonal of a cuboid
= $\sqrt{\text{length}^2 + \text{breadth}^2 + \text{height}^2}$
= $\sqrt{2^2 + 2^2 + 6^2}$
= $\sqrt{4 + 4 + 36}$
= $\sqrt{44}$
= $2\sqrt{11}$ cm
Hence, the correct answer is $2\sqrt{11}$.
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