[tex]\it a+b+c=36\ \ \ \ \ (*)\\ \\ \{a,\ b,\ c\}\ d.\ p.\ \{3,\ 4,\ 5\} \Rightarrow \dfrac{a}{3}=\dfrac{b}{4}=\dfrac{c}{5}=\dfrac{a+b+c}{3+4+5}\ \stackrel{(*)}{=}\ \dfrac{36}{12}=3 \Rightarrow\\ \\ \\ \Rightarrow\ \begin{cases}\it \dfrac{a}{3}=3 \Rightarrow a=3\cdot3=9\\ \\ \it \dfrac{b}{4}=3 \Rightarrow b=4\cdot3=12\\ \\ \it \dfrac{c}{5}=3 \Rightarrow c=5\cdot3=15\end{cases}[/tex]
