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

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

1. R -perimeter.

P Δ ABC = AC + BC + AB = 36 centimeters.

P Δ ABK = AK + BK + AB.

2. BK = 1/2 BC, since the bisector AK, being also the median, divides the BC into equal segments.

ВС = 2ВК.

3. Substitute in the first expression AB instead of AC (the sides are equal according to the condition of the problem) and 2BK instead of BC:

2AB + 2BK = 36 centimeters.

BK + AB = 18 centimeters.

4. Substitute the value of this expression into the formula for calculating P Δ ABK:

P Δ ABK = 10 + 18 = 28 centimeters.