AB=4 means t=4.

∫Rt△ABC，∠B=90，AB=8 cm，BC=6 cm

∴AC= 10 cm

∫PQ∨BC

∴AP /AB =AQ/AC

That is 4/8 = 4x/ 10.

Solution: x = 5/4

(2) When BC∨PQ, △ ABC ∽△ APQ. At this time, it is the same as (1), and x=5/4.

(3) When x=5/4,

∫BC∨PQ，

∴AP/AB =PQ/BC

∴PQ=AP？ BC/AB =6t/8=3/4t，

Then when 0 < t ≤ 4, the overlapping area is s = s △ a ′ pq = s △ apq =1/2ap? PQ= 1/2 t？ 3/4t = 3/8 T2；

When 4 < t ≤ 8, as shown in figure 1, A'p = AP = t, PQ=3/4t,

∴BP=AB-AP=8-t，

Then A'b = t-(8-t)= 2t-8,

∫BD∨PQ，

∴bd/pq=a′b/a′p

∴BD=(2t？ 8)? 3/4t/t =3/2(t-4)，

∴S=S quadrilateral BDQP= 1/2(BD+PQ)? BP= 1/2[3/2(t-4)+3/4 t]？ (8-t=-9/8t2+ 12t-24，

The resolution function is: s = 3/8t2 (0 < t ≤ 4).

S =？ 9/8t2+ 12t？ 24(4