Let's begin by listing out the information given to us:
The 2 triangles are similar. This means that the ratio of the corresponding sides are equal
1.
[tex]\begin{gathered} \frac{|BC|}{|EF|}=\frac{|AB|}{|DE|}\Rightarrow\frac{4}{2.4}=\frac{2}{|DE|} \\ \frac{4}{2.4}=\frac{2}{|DE|} \\ 4\cdot|DE|=2\cdot2.4\Rightarrow4\cdot|DE|=4.8 \\ 4\cdot|DE|=4.8 \\ |DE|=\frac{4.8}{4}=1.2 \\ |DE|=1.2 \end{gathered}[/tex]
2.
[tex]\begin{gathered} \frac{|BC|}{|EF|}=\frac{|AC|}{|DF|}\Rightarrow\frac{4}{2.4}=\frac{|AC|}{3} \\ \frac{4}{2.4}=\frac{|AC|}{3} \\ 2.4\cdot|AC|=3\cdot4 \\ 2.4\cdot|AC|=12 \\ |AC|=\frac{12}{2.4}=5 \\ |AC|=5 \end{gathered}[/tex]
