In triangle ABC, median BM is drawn. Find AM if AC = 44 and BM = 32.

Solution:

The problem states that BM is a median in triangle ABC. By definition, a median connects a vertex to the midpoint of the opposite side. Therefore, M is the midpoint of AC.

• Since M is the midpoint of AC, it divides AC into two equal segments: AM and MC.
• We are given that AC = 44.
• Therefore, AM = MC = AC / 2.
• AM = 44 / 2 = 22.

The length of the median BM (32) is extra information and not needed to find AM.

Answer: 22