In the isosceles triangle ABC, where AB = BC, the bisector AK is drawn. Find the perimeter of the triangle

In the isosceles triangle ABC, where AB = BC, the bisector AK is drawn. Find the perimeter of the triangle ABC if AC = 10 cm, KC = 6 cm.

1. The bisector drawn from the vertex A of the triangle divides the side BC into segments BK and

СK, which are proportional to the adjacent sides AB and СK:

AB / AC = BK / KС.

2. AB = BC according to the problem statement. We take the length of the AB side as x. BK = (x – 6).

3.x / 10 = (x – 6) / 6;

10x – 60 = 6x;

4x = 60;

x = 15.

AB = BC = 15 centimeters.

4. The sum of the three sides of the triangle ABC (perimeter) is equal to: AB + BC + AC = 15 + 15 + 10 = 40 centimeters.

Answer: The perimeter of triangle ABC is 40 centimeters.