A) \[3\frac{1}{2}\,\,cm\]
B) \[4\frac{1}{3}\,\,cm\]
C) \[4\frac{1}{2}\,\,cm\]
D) \[5\frac{1}{3}\,\,cm\]
Correct Answer: B
Solution :
By Pythagoras theorem, \[PR=\sqrt{P{{Q}^{2}}+Q{{R}^{2}}}=\sqrt{{{5}^{2}}+{{12}^{2}}}\] \[=\text{ }13\,\,cm\] \[\because \] O is centroid \[\Rightarrow \] QM is median and M is mid-point of PR. \[QM=PM=\frac{13}{2}\] \[\because \] Centroid divides median in ratio 2: 1. \[\therefore \] \[OQ=\frac{2}{3}QM=\frac{2}{3}\times \frac{13}{2}=\frac{13}{3}\] \[\therefore \] \[OQ=4\frac{1}{3}\,\,cm\]
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