Fie a, b, c lungimile celor trei laturi.
[tex]\it \mathcal{P}=a+b+c=52\ cm\ \ \ \ \ \ (1)\\ \\ \\ \{a,\ b,\ c\}\ d.\ p.\ \{3,\ 4,\ 6\}\ \Rightarrow\ \dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{6}=\dfrac{a+b+c}{3+4+6}\ \stackrel{(1)}{=}\ \dfrac{52}{13}=4\ \ \ \ \ (2)\\ \\ \\ (2) \Rightarrow\begin{cases}\it \dfrac{a}{3}=4 \Rightarrow a=3\cdot4 \Rightarrow a=12\ cm\\ \\ \it \dfrac{b}{4}=4 \Rightarrow b=4\cdot4 \Rightarrow b=16\ cm\\ \\ \it \dfrac{c}{6}=4 \Rightarrow c=6\cdot4 \Rightarrow c=24\ cm \end{cases}[/tex]
