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Could someone help me to understand how can I figure it out, how can I create a formula for finding min/max area of a rectangle inscribed in a rectangle, defined by given width and height. Also if it is possible to be inscribed a rectangle at all.

For a private case, when the rectangle is a square, it is pretty easy using the Pythagorean theorem, but for a common case I'm not sure if the inscribed rectangle is really inscribed.