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 . That is, 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 , is a median and is the centroid, so .

Step - by - Step Solution

1. Find the length of :

Given the ratio and . Let . According to the ratio , substituting into the equation gives .

Cross - multiplying results in