[tex]\displaystyle
34~~~ \text{Aplicam teorema lui Thales} \\
a) \\ \\
\frac{x}{2,66}= \frac{3,2}{2,8} \\ \\
2,8x = 3,2 \times 2,66 \\
2,8x = 8,512 \\ \\
x= \frac{8,512}{2,8} = \boxed{3,04}
[/tex]
[tex]b) \displaystyle \\ \\
\frac{x}{5,7} = \frac{5,76}{5,13} \\ \\
5,13x=5,7 \times 5,76 \\
5,13x=32,832 \\ \\
x= \frac{32,832}{5,13} =\boxed{6,4}[/tex]
[tex]c) \displaystyle \\ \\
\frac{x}{3,92} = \frac{3,6}{4,9} \\ \\
4,9x= 3,6 \times 3,92 \\
4,9x = 14,112 \\ \\
x= \frac{14,112}{4,9} =\boxed{2,88}[/tex]
[tex]35) \displaystyle \\
\text{ I fiecare desen, cele 2 triunghiuri sunt asemenea. } \\
\text{Vom scrie rapoartele de asemanare. }\\
a) \\
\frac{x+1}{8} = \frac{x-0,25}{6} \\ \\
6(x+1) = 8(x-0,25) \\
6x+6=8x-2 \\
8x-6x =6+2 \\
2x=8 \\ \\
x= \frac{8}{2} =\boxed{4}[/tex]
[tex]b) \displaystyle \\ \\
\frac{10}{6} = \frac{x+5}{x+0,2} \\ \\
10(x+0,2)= 6(x+5) \\
10x + 2 = 6x+30 \\
10x-6x=30-2 \\
4x=28 \\ \\
x= \frac{28}{4} =\boxed{7}[/tex]
