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 lengths of  and  given the length of .

Key Concept Explanation

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

Step - by - Step Solution

1. Find the length of :

Given the ratio  and . Let . Then, according to the ratio .

Substituting

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