Geometry

Question Analysis

This question focuses on using the property of a median in a triangle to find the length of a side. The key is to understand that a median bisects the opposite side, which allows us to set up an equation based on the relationship between  and  to find the value of , and then determine the length of .

 

Key Concept Explanation

A median of a triangle is a line segment that joins a vertex to the mid - point of the opposite side. In , since  is a median,  is the mid - point of , so .

 

Step - by - Step Solution

1. Since  is a median of , we know that .

2. We are given that  and .

3. Substitute the expressions into the equation :

.

4. Expand the right - hand side of the equation:

.

5. Solve the equation for :

Subtract  from both sides:

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