[tex]\it \mathcal{P}_{ABC}=18 \Rightarrow AB+BC+AC = 18 \Rightarrow 4+6+AC=18\bigg|_{-10} \Rightarrow AC=8\ cm\\ \\ \\ \mathcal{P}_{DE F}=45\Rightarrow DE+DF+EF = 45 \Rightarrow 10+20+EF=45\bigg|_{-30} \Rightarrow EF=15\ cm[/tex]
[tex]\it \left.\begin{aligned}\ \it\dfrac{AB}{DE}=\dfrac{\ \ 4^{(2}}{10}=\dfrac{2}{5}\\ \\ \it \dfrac{BC}{EF}=\dfrac{\ \ 6^{(3}}{15}=\dfrac{2}{5}\\ \\ \it \dfrac{AC}{DF}=\dfrac{\ \ 8^{(4}}{20}=\dfrac{2}{5} \end{aligned} \right \}\ \stackrel{LLL}{\Longrightarrow}\ \Delta ABC\ \sim\ \Delta DE F[/tex]
