Since triangle ADE is similar to triangle ABC and the scale factor is 2, the following relation must be fulfilled:
[tex]\frac{AD}{AB}=4[/tex]
The, by substituting the given information, we have
[tex]\begin{gathered} \frac{6x-8}{x+2}=4 \\ \end{gathered}[/tex]
By multiplying both sides by x+2, we get
[tex]6x-8=4(x+2)[/tex]
which gives
[tex]6x-8=4x+8[/tex]
Then, by subtracting 4x to both sides, we have
[tex]2x-8=8[/tex]
and by adding 8 to both sides, we obtain
[tex]2x=16[/tex]
then, x is given by
[tex]x=\frac{16}{2}=8[/tex]
Then, by substitutn
