[tex]\it AC=AD+DC=3+6=9\ cm\\ \\ \mathcal{P}_{ABC}=AC+AB+BC=9+12+15=36\ cm\\ \\ DE||AB\ \stackrel{T.f.a.}{\Longrightarrow}\ \Delta CDE\sim \Delta CAB \Rightarrow k=\dfrac{CD}{AC}=\dfrac{\ 6^{(3}}{9}=\dfrac{2}{3}\ (raportul\ de\ asem\breve anare)[/tex]
Raportul perimetrelor a două triunghiuri asemenea este egal
cu raportul de asemănare.
[tex]\it \dfrac{\mathcal{P}_{CDE}}{\mathcal{P}_{CAB}}=k \Rightarrow \dfrac{\mathcal{P}_{CDE}}{36}= \dfrac{2}{3} \Rightarrow \mathcal{P}_{CDE}=\dfrac{36\cdot2}{3}=\dfrac{72}{3}=24\ cm[/tex]
