In triangle ABC, the median BD is the bisector of the triangle. Find the perimeter of triangle ABC

In triangle ABC, the median BD is the bisector of the triangle. Find the perimeter of triangle ABC if the perimeter of triangle ABD is 16 cm and the median BD is 5 cm.

If in triangle ABC the height BD is both the bisector and the median at the same time, then triangle ABC is isosceles. Since the perimeter of a triangle is determined by the sum of all its sides, then AB + AD = 16 – 5 = 11 cm.Since the triangle is isosceles, then AB + AD = BC + CD = 11 cm.It follows that the perimeter of triangle ABC = 11 * 2 = 22 cm.