In the triangle ABC AB = BC = 61, AC = 22 find the length of the median BM.

Since, according to the condition, AB = BC = 61 cm, then the ABC triangle is isosceles, and therefore the median BH coincides with the height, which means that the BM is perpendicular to the AC.

Then AM = CM = AC / 2 = 22/2 = 11 cm.

Consider a right-angled triangle ABM and, by the Pythagorean theorem, define the leg BM.

BM ^ 2 = AB ^ 2 – AM ^ 2 = 61 ^ 2 – 11 ^ 2 = 3721 – 121 = 3600.

BM = √3600 = 60 cm.

Answer: The length of the median BM is 60 cm.