Triangle abc, bh height, cm median, am = 3 cm, ah = hc = 2 cm find the perimeter

Since the segment CM, by condition, is the median of the triangle ABC, then BM = AM = 3 cm, then the length of the side AB = AM + BM = 3 + 3 = 6 cm.

According to the condition, AH = CH = 2 cm, and then the height BH is also the height of the triangle, and therefore the triangle ABC is isosceles with the base AC.

Then AC = AH + CH = 2 + 2 = 4 cm, BC = AB = 6 cm.

Let’s define the perimeter of the triangle ABC.

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

Answer: The perimeter of the triangle is 16 cm.