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The diagram shows a right-angled isosceles triangle $XYZ$ which circumscribes a square $PQRS$. The area of triangle $XYZ$ is $x$. What is the area of square $PQRS$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.  

This problem is taken from the UKMT Mathematical Challenges.
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