question_answer

Find the length of the largest rod that can be placed in a room 16 m long, 12 m broad and \[10\frac{2}{3}\,\,m\] high.

A)  23 m               

B)  68 m

C)  \[22\frac{2}{3}\,\,m\]   

D)  \[22\frac{1}{3}\,\,m\]

Correct Answer: C

Solution :

Length of the largest rod \[=\sqrt{{{L}^{2}}+{{B}^{2}}+{{H}^{2}}}=\sqrt{{{16}^{2}}+{{12}^{2}}+{{\left( \frac{32}{3} \right)}^{2}}}\] \[=\sqrt{256+144+\frac{1029}{9}}\] \[=\sqrt{400+\frac{1029}{9}}\] \[=\sqrt{\frac{3600+1029}{9}}=\sqrt{\frac{4629}{9}}=22\frac{2}{3}\,m\]