Question

Alguém pode me ajudar, é urgente, obrigada ❤️ ​

Answer 1

Teorema de Tales

$a) \: \frac{3}{4} = \frac{x}{8} \\ \\ 4 \cdot x = 8\cdot3 \\ 4x = 24 \\ x = \frac{24}{4} \\ \boxed{ \bf{x = 6} }$

$b) \: \frac{21}{12} = \frac{3x + 1}{2x - 2} \\ \\ 21(2x - 2) = 12(3x + 1) \\ 42x - 42 = 36x + 12 \\ 42x - 36x = 12 + 42 \\ 6x = 54 \\ x = \frac{54}{6} \\ \boxed{ \bf{x = 9} }$

$c) \: \frac{10}{15} = \frac{3x + 1}{5x - 2} \\ \\ 10(5x - 2) = 15(3x + 1) \\ 50x - 20 = 45x + 15 \\ 50x - 45x = 15 + 20 \\ 5x = 35 \\ x = \frac{35}{5} \\ \boxed{ \bf{x = 7} }$

$d) \: \frac{x + 1}{x - 5} = \frac{24}{6} \\ \\ 6(x + 1) = 24(x - 5) \\ 6x + 6 = 24x - 120 \\ 6x - 24x = - 120 - 6 \\ - 18x = - 126 \: \color{red} {\cdot( - 1)} \\ 18x = 126 \\ x = \frac{126}{18} \\ \boxed{ \bf{x =7 } }$

Olá Paola, espero ter ajudado! :)