Question

Determine o valor de x: (utilize a semelhança de triangulos) *​

Answer 1

$\large\boxed{\begin{array}{l}\rm\triangle\,ABC\sim\triangle ADE\\\rm\dfrac{AB}{AD}=\dfrac{AC}{AE}\\\\\rm\dfrac{2+10}{2}=\dfrac{2x-4+5x+10}{2x-4}\\\\\rm\dfrac{12}{2}=\dfrac{7x+6}{2x-4}\\\\\rm 6=\dfrac{7x+6}{2x-4}\\\\\rm 6\cdot(2x-4)=7x+6\\\rm 12x-24=7x+6\\\rm 12x-7x=24+6\\\rm 5x=30\\\rm x=\dfrac{30}{5}\\\\\rm x=6\end{array}}$