Geometry

 

In quadrilateral $PQRS$, $PQ = QR = RS = SP$, $PR = \sqrt{2}$, and $QS = \sqrt{2}$. Find the perimeter of $PQRS$.   

 

All four sides are equal; that makes it at least a rhombus.  

Both diagonals are the same; and that makes it a square.   

 

The diagonal of the square is the square root of two. 

That makes the sides equal one.  Therefore the perimeter is 4 units.    

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