question_answer

If G is the centroid and AD is the median of \[\Delta ABC\]and\[AG=4\,\,cm,\]then DG is equal to[SSC (CGL) 2014]

A) \[2\,\,cm\]

B) \[3\,\,cm\]

C) \[4\,\,cm\]                     

D) \[5\,\,cm\]

Correct Answer: A

Solution :

G is the centroid, i.e. G is the point of intersection of medians as shown in the figure below

In \[\Delta ABC,\] AD is the median and G is centroid.

We know that, medians intersect each other such that each median split in the ratio of 1: 2 from the base side.

\[\therefore \]      \[\frac{GD}{AG}=\frac{1}{2}\]

\[\Rightarrow \]   \[GD=\frac{1}{2}\times AG\]

\[=\frac{1}{2}\times 4=2\,\,cm\]\[[\because AG=4\,\,cm]\]

\[\therefore \]Value of DG = 2 cm