In the triangle ABC AB = BC = 95, AC = 114. Find the length of the median BM.

In the condition AB = BC = 95, then this triangle is isosceles with the base AC = 114. The median BM in an isosceles triangle is also the height that divides the AC in half, which means that a right-angled triangle ABM is formed, in which the hypotenuse AB = 95, leg AM = AC: 2 = 114: 2 = 57. According to the properties of a right-angled triangle AB ^ 2 = BM ^ 2 + AM ^ 2. So BM = √ (AB ^ 2 – AM ^ 2) = √ (9025 – 3249) = 76.