[tex]\it \left.\begin{aligned} \it \dfrac{NJ}{JL}= \dfrac{\ 6^{(3}}{9} = \dfrac{2}{3}\\ \\ \\ \it \dfrac{NK}{KM}= \dfrac{\ 10^{(5}}{15} = \dfrac{2}{3} \end{aligned}\right\} \stackrel{R.T.Thales}{\Longrightarrow}\ \ JK||LM[/tex]
[tex]\it NM=NK+KM=6+9=15\\ \\ NL=NJ+KL=10+15=25[/tex]
Comparăm triunghiurile NML și NKJ:
[tex]\it \left.\begin{aligned}\it\dfrac{NM}{NK}= \dfrac{25}{10}=2,5\\ \\ \it\widehat N =\ unghi\ \ comun\\ \\ \it\dfrac{NL}{LJ} = \dfrac{15}{6} =2,5 \end{alignrd}\right\}\ \stackrel{LUL}{\Longrightarrow}\ \Delta NML\sim\Delta NKJ \Rightarrow \dfrac{LM}{JK} = 2,5 \Rightarrow\\ \\ \\ \Rightarrow \dfrac{30}{JK}=2,5 \Rightarrow JK= \dfrac{30}{2,5} = \dfrac{300}{25}=12[/tex]
