Question

Points B, D, and F are midpoints of the sides of triangle ACE. EC = 38 and DF = 16. Find AC. The diagram is not to scale.

Answer 1

You are correct. DF is half as long as AC since DF is the parallel midsegment to AC

AC = 2*DF
AC = 2*16
AC = 32

The info about EC = 38 is extra info most likely put in there to throw you off, or as a distraction.

Answer 2

Answer:  Yes, the answer 32 is correct.  

Explanation: Since, According to the mid point theorem, the line segment connecting the midpoints of the two sides of a triangle is parallel to the third side and is half of the third side of triangle.

Here, FD is the line segment connecting to the midpoints F and D and it is parallel and half of the third side AC.

Thus, FD=AC/2⇒ AC=2FD

But, according to the question, FD=16 so, AC=2×16=32

Thus, AC=32 unit will be the answer.