In an isosceles triangle ABC AB = BC = 61 and base AC = 22. Find the length of the median BM.

Given: AB = BC = 61
AC = 22
Find: BM
Decision.
In an isosceles triangle, the median to the base is the height and bisector and is calculated by the formula
L = √a²-b² / 4 (where L is the height, median, bisector, and are equal sides of the triangle, b is the base of the triangle)
I.e
L-BM, a = AB = BC = 61, b = AC = 22
From here
BM = √AB²-AC² / 4
BM = √61²-22² / 4
BM = √3721-484 / 4
BM = √3600
BM = 60
Answer: median length BM = 60.