In triangle ABC AB = BC = 53, AC = 56. Find the length of the median BM.

1. We calculate the length of the segment AM, taking into account that the median BM divides the side of the AC, to which it is drawn, into two identical segments:

AM = AC / 2 = 56: 2 = 28 units.

2. Since the median BM is drawn to the base of the isosceles triangle, it also performs the function of height. That is, triangle ABM is rectangular.

3. We calculate the length of the BM:

ВM = √AB² – AM² = √53² – 28² = √2809 – 784 = √2025 = 45 units of measurement.

Answer: the length of the ВM is 45 units.