GK_Gmat wrote:

Fig wrote:

(A) too

If BQ = CR = DS = AP, then the shapes of the 4 pieces are the same. That implies PR and QS are composed of 1 long and 1 small "interior" sides.

And so, PR = QS.

The fact that we know the perimeter is useless...

Fig, can you pls. explain how you go from 'BQ = CR = DS = AP' to 'the shapes of the 4 pieces are the same'

If BQ = CR = DS = AP, then QC = RD = AS = PB, since it is a square. How do you proceed from here?

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.