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 set up an equation involving , and then find the length of .

 

Key Concept Explanation

The centroid of a triangle divides each median in the ratio . In , since  is the centroid and  is a median, , which also means  and .

 

Step - by - Step Solution

1. Set up the equation based on the centroid - median ratio:

Since  and , we can express  in terms of  as .

Given  and , substitute into the equation .

So, .

2. Solve the equation for :

First, expand the right - hand side: