Current location - Training Enrollment Network - Mathematics courses - The moving point problem of mathematics in the last semester of the second day of junior high school
The moving point problem of mathematics in the last semester of the second day of junior high school
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.