[tex]Notam\ laturile\ cu\ a,b\ si\ c.\\
\{a,b,c\}d.p.\{4,5,6\}\Rightarrow \frac{a}{4}=\frac{b}{5}=\frac{c}{6}=k\Rightarrow a=4k,b=5k,c=6k\\
P=45\\
a+b+c=45\\
4k+5k+6k=45\\
15k=45\Rightarrow \boxed{k=3}\\
a=4k\Rightarrow \boxed{a=12}\\
b=5k\Rightarrow \boxed{b=15}\\
c=6k\Rightarrow \boxed{c=18}[/tex]
