In the isosceles triangle ABC with the base BC, the median AM is drawn. find the median AM

In the isosceles triangle ABC with the base BC, the median AM is drawn. find the median AM if the perimeter of the triangle ABC = 32 cm, and the perimeter of the triangle ABM = 25 cm.

1. The perimeter of the triangle ABM = AB + BM + AM = 25 cm.

2. The perimeter of the triangle ABC = AB + BC + AC = 32 cm.

3. AB = AC as the lateral sides of an isosceles triangle.

4. BM = CM, since the median divides the BC into two equal parts.

5. BM + CM = BC. ВС = 2ВМ.

6. Substituting AB instead of AC and 2BM instead of BC into the second formula:

2АВ + 2ВМ = 32 cm.Divide this expression by 2:

AB + BM = 16 cm. Substitute the value of this expression in the first formula:

16 + AM = 25 cm.

AM = 25 – 16 = 9 cm.

Answer: the median AM is 9 cm.