Question

I'm unable to solve this problem

Answer 1

ABCD is a rectangle.  P is on AD.   Q is on AB.
PR is drawn || AB.  QS is drawn || to AD.
As AB ⊥ QS, AB ⊥ AD,   we have AD || QS.
As PR ⊥ AD ,  PR ⊥ BC,  we PR || AB.

PR and QS intersect at O.

So we have  OQ || PA, and PO || AQ.    So APOQ is a parallelogram.
As the angles between adjacent sides are 90 deg., APOQ is a rectangle.

We also have : AP = OQ = BR = 1/4 * BC
                         AQ = PO = DS = 1/4 * CD

Area of  APOQ = AP * PO = 1/16 *  BC * CD
Area of ABCD =  AD * AB =  AD * DC =  BC * CD

Hence,  the ratio of areas :    1/16 :  1   or    1 : 16