Question

How do I get to the answer of this question?

Answer 1

Looking at the image, we can see that the proportion between EA and AB is the same proportion between FA and AC:

`\begin{gathered} (EA)/(AB)=(FA)/(AC) \\ (40)/(80)=(50)/(100)=(1)/(2) \end{gathered}`

Also the angles EAF and BAC are congruent, since they are vertical angles.

Therefore, the triangles ABC and AEF are similar triangles by case SAS, and the length of side EF is:

`\begin{gathered} (EF)/(BC)=(1)/(2) \\ (EF)/(120)=(1)/(2) \\ EF=(120)/(2)=60 \end{gathered}`

Correct option: d