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Ans A
Since BQ = CR = SD = AP ;
As sides of a square are equal :
PB = AS = DR = QC
Again each angle i.e B , C , D , A must be 90(angles of a square)
hence their opp angles must be 90. So figures are actually rectangles with PR = QS

Well, I can try

As BQ = CR = DS = AP, we know that QC = RD = SA = BP because we have a square with each side thus equal.

Then, at this point, we know that the triangles BQP, QCR, RDS and SAP are right similar triangles.

That implies that PQ=QR=RS=SP.

In addition, each angle of PQRS are rights by the following reasonning:
o angle(PQR) = 180 - angle(BQP) - angle(RQC)
= 180 - (90-angle(BPQ)) - angle(RQC) as BQP is a right triangle
= 90 + angle(BPQ) - angle(RQC)
= 90 + angle(BPQ) - angle(BPQ) as BPQ and RQC are similar triangles
= 90

We are thus now with PQRS definied by:
o 4 equal sides
o 4 right angles

It's the definition of a square and that means its diagonals PR and QS are equal.

Faster taped than I did

the OA is (A)