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Squaring a Rectangle (PST Version)

You are given a square and a rectangle with the same area. Explore the applet to find a process on how the rectangle can be turned into a square of the same area.
Use a standardized starting configuration: S = 36 and Xn = 9. Answer the questions below.

What changes and what remains the same when Xn changes?

Predict what Next iteration will do (write your prediction), then click it twice to verify it.

How is determined?