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:
[tex]\frac{ED}{DF}=\frac{EC}{CA}[/tex]
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:
[tex]\frac{19.5}{18}=\frac{39}{CA}\\19.5CA=18*39\\19.5CA=702\\CA=\frac{702}{19.5}CA=36[/tex]
Hence, AC = 36
