Geometry

Question Analysis

This question focuses on applying the properties of the centroid of a triangle. The main task 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: .

Multiply both sides of the equation by to get rid of the fraction:

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