Question

In the accompanying diagram, AABC ~ADEF, AB = 12, AC = 8, DE = x, and DF = 2. Find the value of x.

Answer 1

Using the similarity ratio for sides of the given triangles,

$\begin{gathered} \frac{AB}{DE}=\frac{AC}{DF} \\ \frac{12}{x}=\frac{8}{2} \\ x=\frac{12}{4} \\ x=3 \end{gathered}$