Geometry

Question Analysis

This question focuses on applying the properties of the centroid of a triangle. The key is to use the ratio in which the centroid divides the median to find the length of  given the length of .

 

Key Concept Explanation

The centroid of a triangle is the point of intersection of its medians. A median connects a vertex to the mid - point of the opposite side. The centroid divides each median in the ratio , meaning the segment from the vertex to the centroid is twice as long as the segment from the centroid to the mid - point of the side.

 

Step - by - Step Solution

1. Since  is the centroid of  and  is part of a median (assuming  is the mid - point of ), the centroid  divides  such that . So, , and . Then

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