For RH vertical PQ, the vertical foot is H, connected with MN, ∠BAG=∠MAE, and the extension line of AG-NB is G, which proves that △ Bag △ EAM, BG = Me, Ag = AM, △ Man △ Gan, Mn = GN,

RH=ME= 1/2*( 12-3t)，

NB = HA = 8-2t- 1/2 *( 12-3t)= 2- 1/2 * t，

Fn = 3-nb = 1+ 1/2 * t，FM = 3-me = 1/2 * (3t-6)，Mn = gn = nb+BG = 2- 1/2 * t+66。

So the square of (8-2t) = 1+ 1/2 * t+1/2 * 3t-3.

The solution is t=8-2√7.