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.
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