[tex]\displaystyle\\
\text{Aplicam reciproca teoremei lui Thales, pentru a vedea daca }EF||BC \\ \\
\text{Verificam daca: }~~ \frac{AE}{EB}= \frac{AF}{FC} \\ \\
\frac{AE}{EB}=\frac{1500}{1000} = \frac{15}{10} = \boxed{\frac{3}{2}} \\ \\
\frac{AF}{FC} = \frac{1200}{800} =\frac{12}{8} =\boxed{\frac{3}{2}} \\ \\
\Longrightarrow~~\frac{AE}{EB}= \frac{AF}{FC} =\frac{3}{2} ~~\Longrightarrow~~ \boxed{EF ~|| ~BC} [/tex]
[tex]\displaystyle\\
\text{Calculam lungimea segmentului AB.} \\ \\
AB = AE+EB=1500+1000 =\boxed{2500~m}\\\\
\text{Aplicam teorema lui Thales pentru a calcula lungimea gardului }AB. \\\\
\frac{AE}{AB} = \frac{EF}{BC} \\ \\
\frac{1500}{2500} = \frac{EF}{3000} \\ \\
EF =\frac{3000\times1500}{2500} =\frac{3000\times15}{25} = \frac{3000\times3}{5} =600 \times 3 = \boxed{\boxed{1800~m}}[/tex]
