Finding the Length of a Median in Triangle ABC

Consider triangle ABC with sides of lengths 7, 24, and 25. A line segment is drawn from point A to the midpoint of side BC. Let D be the midpoint of side BC. Calculate the length of segment AD.

Recall that the length of a median in a triangle can be calculated using the formula:

$$m_a = \sqrt{\f\frac{2b^2 + 2c^2 - a^2}{4}}$$

where m_a is the length of the median from vertex A to side BC, and the lengths a, b, and c are the lengths of the sides opposite vertices A, B, and C respectively.