Question

In triangle ABC, E is the midpoint of AC and D is the midpoint of CB. if DF is parallel to BE, find the length of side AB.

Answer 1

Δ FCD is a right triangle ( 3² + 4² + 5² ).
10 : EB = 5 : 3
5 EB = 30
EB = 6
With Pythagorean theorem:
CE² = 10² - 6² = 10 - 36 = 64
CE = 8
ED = 5
AB = 2 · 5 = 10
Answer: The length of the side AB is 10. 

Answer 2

I hope this helps you