[tex]\it \mathcal{P}=2(L+\ell)=28\bigg|_{:2} \Rightarrow L+\ell=14\ \ \ \ \ \ (*)\\ \\ \\ \{\ell,\ \ L\}\ d.\ p.\ \{3,\ 4\} \Rightarrow \dfrac{\ell}{3}=\dfrac{L}{4}=\dfrac{\ell+L}{3+4}\ \stackrel{(*)}{=}\ \dfrac{14}{7}=2\\ \\ \\ \dfrac{\ell}{3}=2 \Rightarrow \ell=2\cdot3=6\ cm\\ \\ \\ \dfrac{L}{4}=2 \Rightarrow L=2\cdot4=8\ cm\\ \\ \\ \mathcal{A}=L\cdot \ell=8\cdot6=48\ cm^2[/tex]
