Question

let ABCD be a square locate points pqrs on the sides ab BC CD da respectively such that AP = PQ = PR = 30 prove that pqrs is a square

Answer 1

According to you PQ = PR but still to prove PQRS as a square we need all angels 90° but there is a contradiction PR is the diagonal of PQRS wher PQ is a side containing the right angle .Which is Angle PQR as we want it to be a square.
But PR is the hypotenuse and cannot be = to PQ as it is a side .
So by Traingle inequality process we can say the question to be wrong.
Hope this will help you.
With a HOPE that my prediction is correct.
THANKS