- What does the rectangle look like at the extremes?
- Will the side be greater than or less than the diameter?
- What fraction of the side length of the square do you think the diameter will be?
Opening the sketch and dragging the point, without showing the measurements, is interesting. How close is a student's guess about where the position of the drag point must be for the rectangle to be a square? How close is there estimation of the relationship between the square's side and the diameter?
Lastly, they could choose an arbitrary diameter, like 100, and see if they can verify the result. Surprisingly, everything comes out nice and evenly with narry a square root of two in sight!