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For the initial question:
Are any rectangles too long?
Do any rectangles share the same width or height?
For the final question:
What must the areas of the five rectangles add up to?
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?