Line segment AM is the bisector of triangle ABC, AB = 48 cm, AC = 32 cm, BM = 18 cm Find side BC.

It is known from the condition that the segment AM is the bisector of the triangle ABC.

We also know that:

AB = 48 cm;

AC = 32 cm;

BM = 18 cm.

You need to find: BC -?

The first step is to apply the property of the bisector of a triangle and write down the ratio:

AB / AC = BM / MC;

We express from the ratio MC:

MC = (AC * BM) / AB.

Substitute the values and calculate:

MC = (32 * 18) / 48 = 12 cm.

The side of the triangle BC consists of the sum of the two line segments BM and MC.

Let’s find the length BC = BM + MC = 18 + 12 = 30 cm.

Answer: BC side = 30 cm.