In triangle ABC AB = BC = 53, AC = 56 find the length of the median BM.

In triangle ABC it is known:

AB = BC = 53;
AC = 56.
Find the length of the median BM.

Solution.

1) In a triangle, 2 sides are equal, which means the triangle is isosceles. The median divides the side in half, which means that the values of the sides AM and MC are known.

AM = MC = 1/2 * 56 = 56/2 = 50/2 + 6/2 = 25 + 3 = 28;

2) In an isosceles triangle, the median drawn from point B is also the height.

3) Consider a triangle ABM with a right angle M.

If the hypotenuse AB = 53 and the leg AM = 28 are known, then we will find the second leg ВM.

BM = √ (53 ^ 2 – 28 ^ 2) = √ ((53 – 28) * (53 + 28)) = √ (25 * 81) = 5 * 9 = 45.

Answer: median BM = 45.