Given: △ABC,

ADEF rhombus

D∈AB

, E∈BC

, F∈AC

AB=14, BC=12, AC=10

Find: BE and EC

BE = 7 EC = 5

Step-by-step explanation:

Diagonal AE of the rhombus is the angle bisector of angle A. As such, it divides the segments of triangle ABC on each side so they're proportional to the segments on the other side. That means ...

BE/EC = BA/CA = 14/10 = 7/5

We know that BE + EC = BC = 12. This happens to be the sum of the ratio units (7+5), so we can conclude ...

BE = 7

EC = 5