In triangle ABC, the height BH and the median CM are plotted. Find the perimeter of the triangle

In triangle ABC, the height BH and the median CM are plotted. Find the perimeter of the triangle ABC if AM = 3, AH = HC = 2.

The height BH is drawn to the AC side, and since, according to the condition, AH = CH, then BH is also the median of the triangle ABC.

Since the height and the median coincide, the ABC triangle is isosceles with the AC base.

Side length АС = АН + НС = 2 + 2 = 4 cm.

Since CM is the median, then BM = AM = 3 cm, then AB = AM + BM = 3 + 3 = 6 cm.

BC = AB = 6 cm.

Then Ravs = AB + BC + AC = 6 + 6 + 4 = 16 cm.

Answer: The perimeter of triangle ABC is 16 cm.