[tex]\it \mathcal{P} =2\cdot(L+\ell) =96|_{:2} \Rightarrow L+\ell=48\ \ \ \ \ (1)\\ \\ \ell=\dfrac{3}{5}\ din\ L \Rightarrow \ell=\dfrac{3}{5}\cdot L|_{\cdot5}\Rightarrow5\ell=3L|_{+3\ell} \Rightarrow 8\ell=3L+3\ell \Rightarrow\\ \\ \\ \Rightarrow8\ell=3\cdot(L+\ell) \stackrel{(1)}{\Longrightarrow} 8\ell=3\cdot48|_{:8}\Rightarrow\ell=3\cdot6 \Rightarrow \ell=18\ cm\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow L+18=48 \Rightarrow L=48-18 \Rightarrow L=30\ cm\\ \\ \\ \mathcal{A} =L\cdot \ell=30\cdot18=540\ cm^2[/tex]
