In an isosceles triangle ABC, the median AD is drawn. If the perimeter of the triangle ABC = 50 cm, and the

In an isosceles triangle ABC, the median AD is drawn. If the perimeter of the triangle ABC = 50 cm, and the perimeter of the triangle ABD = 30 cm, then the length of AD is?

1. AB = AC, since the given triangle is isosceles.

2. The perimeter of the triangle ABC = AB + BC + AC = 50 cm.

3. Median AD divides the BC side into two equal segments. Therefore, BC = 2BD.

We replace in the original expression AC with AB and BC with 2BD:

2AB + 2BD = 50 cm.

AB + BD = 25 cm.

4. The perimeter of the triangle ABD = AB + BD + AD = 30 cm.

We substitute here the value AB + BD = 25 cm:

25 + AD = 30 cm. AD = 5 cm.

Answer: AD = 5 cm.