Question

Teorema de tales, pra hojeee me ajudem

Answer 1

Pelo Teorema de Tales:

$\dfrac{6}{10}=\dfrac{2x}{3x+5}\\\\ 6(3x+5)=10\cdot2x\\\\ 18x+30=20x\\\\ 2x=30\\\\ x=\dfrac{30}{2}\\\\ \boxed{x=15}$

Novamente por esse teorema:

$\dfrac{10}{y}=\dfrac{3x+5}{4}\\\\ 10\cdot4=y(3x+5)\\\\ 40=y(3x+5)$

Substituindo o valor obtido para x:

$40=y(3x+5)\\\\ 40=y(3\cdot15+5)\\\\ 40=y(45+5)\\\\ 50y=40\\\\ y=\dfrac{40}{50}\\\\ \boxed{y=\dfrac{4}{5}}$