[tex]\text {Raportul ariilor a doua patrate = raportul patratelor } \\ \text {laturilor = raportul patratelor perimetrelor celor doua patrate. } \\ \\ \frac{A_1}{A_2}= \frac{L_1^2}{L_2^2}= \frac{P_1^2}{P_2^2} \\ \\ =\ \textgreater \ \;\;\; \frac{P_1}{P_2}= \frac{\sqrt{A_1}}{\sqrt{A_2}}=\frac{\sqrt{4}}{\sqrt{1}}=\frac{2}{1} \\ \\ =\ \textgreater \ \;\text{Lungimile celor 2 bucati de sarma, sunt direct prop. cu 2 si 1 } \\ \text{iar suma lor este de 5 metri} [/tex]
[tex]Rezolvare: \\ \\ \frac{x}{2} = \frac{y}{1} =k~~~~~=\ \textgreater \ ~~x=2k~~~si~~~y=k \\ x+y=5 \\ 2k+k=5 \\ 3k=5 \\ k= \frac{5}{3} \\ x=2k=2~\cdot~\frac{5}{3}=\frac{10}{3}~m = \boxed{3,(3)~m~~(lungimea ~partii ~mai~ mari)} \\ \\ y=k=\frac{5}{3}~m = \boxed{1,(6)~m~~(lungimea ~partii ~mai~ mici)}[/tex]
