In triangle ABC, it is known that AB = BC = 65, AC = 50. Find the length of the median BM.

Solution:

AB = BC = 65 – isosceles triangle.

Let’s use the formula for finding the length of the median of an isosceles triangle:

m = 1/2 × √ (4a ^ 2 – c ^ 2), where a is the side of the triangle, c is the base of the triangle,

those. a = AB, c = AC, m = BM.

We get:

BM = 1/2 × √ (4 × (65) ^ 2 – (50) ^ 2);

BM = 1/2 × √ (14400);

ВM = 1/2 × 120;

ВM = 60.

Answer: ВM = 60.