The median BD of a triangle ABC splits it into two triangles, the perimeters of which are 32cm

The median BD of a triangle ABC splits it into two triangles, the perimeters of which are 32cm and 36cm. Find ABC the perimeter of the triangle if BD = 10cm.

Consider two triangles into which triangle ABC splits the median BD. Triangle ABD and triangle DBC.

The perimeter of the triangle ABD = P1 is equal to AB + BD + AD = 32 centimeters.

The perimeter of the triangle DВС = P2 is equal to DB + BC + CD = 36 centimeters.

The perimeter of the triangle ABC is equal to AB + BC + AC = P1 + P2 – 2 * BD.

Let’s answer the question of the problem.

1). Let’s find what the perimeter of the triangle ABC is equal to.

32 + 36 – 2 * 10 = 68 – 20 = 48 centimeters.

Answer: The perimeter of triangle ABc is 48 centimeters.