Triangles ABC and A'B'C are similar. This means that the corresponding sides are in the same ratio, in this case:
[tex]\frac{BC}{B^{\prime}C}=\frac{AC}{A^{\prime}C}=\frac{AB}{A^{\prime}B^{\prime}}[/tex]
Replacing with data:
[tex]\begin{gathered} \frac{9}{6}=\frac{12}{A^{\prime}B^{\prime}} \\ 9\cdot A^{\prime}B^{\prime}=12\cdot6 \\ A^{\prime}B^{\prime}=\frac{72}{9} \\ A^{\prime}B^{\prime}=8 \end{gathered}[/tex]
