In the triangle ABC AB = BC = 75 AC = 120 find the length of the median BM.

1. The sides of the triangle AB and BC are equal to each other, hence the triangle ABC is isosceles.

2. AM = CM = 120: 2 = 60 cm, since the median BM divides the base into two equal segments.

3. The median drawn to the base is also the height. The BMC angle is straight.

4. Using the formula of the Pythagorean theorem, we calculate the length of the median BM, which in the BCM triangle is a leg:

BM = √BC ^ 2 – CM ^ 2 = √75 ^ 2 – 60 ^ 2 = √5625 – 3600 = √2025 = 45 cm.

Answer: the length of the median BM is 45 cm.