Yangzhou city), as shown in the figure, in the right-angle ABCD, AD = 3cm, AB = a cm (a > 3). Moving points M and N start from point B at the same time and move along B→A and B→C, respectively, with the speed of1cm/s. When crossing M, there is a straight line perpendicular to AB, and points AN and CD intersect at P and Q respectively.

(2) If a = 5cm, find the time t for making △PNB∽△PAD, and find their similarity ratio;

Because △PNB∽△PAD, BN:AD=PN:AP.

Because MQ//AD//BC, PN:AP=BM:AM,

So BM:AM=BN:AD,

And BM =1* t = bn = t.

AM=5-t

AD=3，

Replaced:

t:(5-t)=t:3

t=2

Because 2

So the solution is:

t=2

The similarity ratio is equal to 2:3.