Given an isosceles triangle ABC, in which AB = AC, its perimeter is 36 cm

Given an isosceles triangle ABC, in which AB = AC, its perimeter is 36 cm. The bisector of AK is 10 cm. Find the perimeter of triangle ABK.

1. Let us denote the perimeter by the symbol P.

2. P of triangle ABK = AB + BK + AK.

3. The bisector AK in an isosceles triangle also performs the functions of the median, that is, it divides the side to which it is drawn into segments of the same length:

BK = SK. Therefore, BC = 2 BK.

4. P triangle ABC = AB + AC + BC = 36 centimeters. We replace AC with AB (AB = AC according to the condition of the problem) and BC with 2 ВC:

2AB + 2BK = 36 centimeters.

AB + BK = 18 centimeters.

5. P triangle ABK = 18 + 10 = 28 centimeters.