In the figure given below, BA, FE and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm.
Calculate EF and AC.
I think the answer is EF= 8.66 and AC = 25.66 but I have no way to verify since my textbook doesn't have the answer. So could someone solve it and verify if my answer is right. Thanks in advance.
On
Using a construction in Cinderella, I get $EF=9$ and $AC=25$.
For the former, observe that $\triangle CDG$ is similar to $\triangle EFG$. For the latter, consider $\triangle CEF$ and $\triangle CAB$ which are similar to one another as well. So with the $EF$ you got before, and knowing $CE$, you get $AC$.
Note that your whole construction still has some freedom in it. It isn't fully determined by the constraints you stated, but the lengths you are asking about don't depend on how you make that free choice.
The lngths are as follows $EF=9$, $AC=225/9=25$