Question

Observe a figura r // s // t. Calcule o valor de X de acordo com o teorema de Tales

Answer 1

$\frac{2x+2}{6x} = \frac{2x+4}{2x+12} \\ \\ \frac{2(x+1)}{6x} = \frac{2(x+2)}{2(x+6)} \\ \\ \frac{x+1}{3x} = \frac{x+2}{x+6} \\ \\ Multiplica~cruzado \\ \\ 3x(x+2) = (x+1)(x+6) \\ 3x^2+6x=x^2+6x+x+6 \\ 2x^2-x-6=0$

$\Delta = (-1)^2-4(2)(-6) \\ \Delta = 1 + 48 \\ \Delta = 49 \\ \\ \\ x = \frac{1~\pm~7}{4} \\ x' = \frac{1~+~7}{4} =2 \\ x''= \frac{1-7}{4} = \frac{-3}{2} ~\rightarrow~nao~convem$



S = {2}