解:由條件知:?$ AP= 2t,$??$QD=t,$??$AQ=6-t,$??$∠B=∠PAQ = 90°$?
?$(1)$?當(dāng)?$\frac {AQ}{BC}=\frac {AP}{AB}$?時(shí),?$△AQP∽△BCA$?
∴?$\frac {6-t}{6} =\frac {2t}{12}$?
∴?$t=3$?
?$(2)$?當(dāng)?$\frac {AQ}{AB}=\frac {AP}{BC}$?時(shí),?$△APQ∽△BCA$?
∴?$\frac {6-t}{12}=\frac {2t}{6}$?
∴?$t=\frac {6}{5}$?