Since PQ and BC are parallel, we have the following:
That is to say, triangles APQ and ABC are similar. Since they are similar, their sides are proportinal. We can then see this relation in the following equation:
[tex]\frac{12+6}{6}=\frac{18+x}{x}[/tex]
Where x is the lenght of AQ. We know rearrange the equation
[tex]\frac{18}{6}=\frac{18+x}{x}[/tex][tex]3=\frac{18+x}{x}[/tex][tex]3x=18+x[/tex][tex]2x=18[/tex][tex]x=9[/tex]
And so, the lenght of AQ is 9
