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This initial task is fairly straightforward. It can be solved analytically by just considering the given, 'static' diagram. However, it is quite nice to first look at some of the movies on the next four pages, which show how the square changes as one or other side of the rectangle changes. The way the square changes may come as a surprise!

It might be thought that the movies would reveal that there is a simple direct or inverse relation between the area of the square and each side of the rectangle. However, it turns out that the relation involves differences.
The movies allow students to adopt an empirical approach if they so wish, but they can also be used to support an analytic approach, ie one based on geometric relations rather than just on observed numerical values. Either way, it helps to focus on the diagonals of the square.

The movie on the next page shows what happens as the vertical side of rectangle ABCD changes.

NOTE: you can, at any stage, use this JAVA worksheet to explore the task in a more interactive way.

FREE:
a high-res pdf file of this new GEOaa-zz task