Square in a triangle

Weekly Problem 33 - 2006
A square is inscribed in an isoscles right angled triangle of area $x$. What is the area of the square?

Problem



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

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Square in a Triangle