In triangle ABC, it is known that AB = 10 cm, BC = 4 cm, CA = 8 cm. On the side AC there is a point D

In triangle ABC, it is known that AB = 10 cm, BC = 4 cm, CA = 8 cm. On the side AC there is a point D such that AD = 6 cm. What is the segment BD.

Consider triangles ABC and DBC with a common angle C. They are similar in angle and two sides, related to each other in the same 2: 1 ratio. In other words, the parties relate to each other:

AC / CB = BC / DC = AB / BD, in specific values: 8/4 = 4/2 = 10 / BD = 2

Thus, BD = 10/2 = 5 (cm).