Fie x, y, z lungimile laturilor triunghiului.
Perimetrul este:
[tex]\it \mathcal{P} = x+y+z=48\ \ \ \ \ (1)\\ \\ \{x,y,z\} \sim\{3,4,5\} \Rightarrow \dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=\dfrac{x+y+z}{3+4+5}\ \stackrel{(1)}{=}\ \dfrac{48}{12}=4\ \ \ \ \ (2)[/tex]
[tex]\it (2) \Longrightarrow \begin{cases}\it \dfrac{x}{3}=4\Rightarrow x=3\cdot4=12\\ \\ \it \dfrac{y}{4}=4\Rightarrow y=4\cdot4=16\\ \\ \it \dfrac{z}{5}=4\Rightarrow z=5\cdot4=20\end{cases}[/tex]
