Finding the length of DE

DE = 6

Step-by-step explanation:

Let's consider some theorem:

1- The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to equal to half of it

2. A straight line through the mid point of one side of a triangle parallel to a second side bisects the third side.

Having noted that, let's see that;

∆ ABC is similar to ∆ BAC

Therefore, from the above theorem and the information given,

(DE / AC) = ( BE / BC)

From the question, BC is 10

Therefore,

(DE/12) = (5 / 10)

Cross multiplying:

10*DE = 12*5

10DE = 60

DE = 60/10

DE = 6

Hope that helped.