Answer:
36
Step-by-step explanation:
Triangle FED and Triangle AEC are similar.
That means, the ratio of corresponding sides are equal. Thus we can say:
![\frac{ED}{DF}=\frac{EC}{CA}](https://tex.z-dn.net/?f=%5Cfrac%7BED%7D%7BDF%7D%3D%5Cfrac%7BEC%7D%7BCA%7D)
Also, since EC is 39 and D is the midpoint, ED and DC are half of that. Hence ED = 39/2 = 19.5
Now we can use the ratio to solve for AC:
![\frac{19.5}{18}=\frac{39}{CA}\\19.5CA=18*39\\19.5CA=702\\CA=\frac{702}{19.5}CA=36](https://tex.z-dn.net/?f=%5Cfrac%7B19.5%7D%7B18%7D%3D%5Cfrac%7B39%7D%7BCA%7D%5C%5C19.5CA%3D18%2A39%5C%5C19.5CA%3D702%5C%5CCA%3D%5Cfrac%7B702%7D%7B19.5%7DCA%3D36)
Hence, AC = 36