Question

sabendo que as retas a, b e c são paralelas, utilize o teorema de tales e marque abaixo o valor encontrado para X
A ( ) X= 3
B ( ) X= 4
C ( ) X = 5
D ( ) X = 6 ​

Answer 1

Teorema de Tales:

$\frac{3x}{x + 6} = \frac{x + 3}{x} \\ \\ 3 {x}^{2} = (x + 3)(x + 6) = \\ {3x}^{2} = {x}^{2} + 9x + 18 \\ 2x {}^{2} - 9x - 18 = 0 \\ </p><p>Δ = ( - 9) {}^{2} - 4 \times 2( - 18) \\ </p><p>Δ = 81 + 144 \\ </p><p>\boxed{\boxed{Δ = 225}}$

$x = \frac{ - ( - 9)± \sqrt{225} }{4} \\ \\ x1 = \frac{9 + 15}{4} = \frac{24}{4} = 6 \\ \\ x2 = \frac{9 - 15}{4} = - \frac{ 6}{4} = - \frac{3}{2} \\ \\ \boxed{\boxed{x1 = 6}} \\ x2 = - \frac{3}{2}$

""Alternativa D""

 ✿~Sah