Geometry

Question Analysis

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

 

Key Concept Explanation

The centroid of a triangle is the point of intersection of the medians. A median of a triangle is a line segment that joins a vertex to the mid - point of the opposite side. The centroid divides each median in the ratio , with the longer segment being from the vertex to the centroid and the shorter segment being from the centroid to the mid - point of the side.

 

Step - by - Step Solution

1. Recall the property of the centroid: The centroid  divides the median  such that , which means  and . So, .

2. Given that

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