24-SquareRectangle

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You may drag any of the red points, and the construction will adjust accordingly.

** Explanation of the construction: **
We need a length s such that s^2 = AB*BC. This can be written s/AB = BC/s, which suggests
similar triangles. The triangle AGE has a right angle at G, being inscribed in a semicircle,
and triangles ABG and GBE are right triangles similar to it and thus each other.
We have thus equal ratios of short leg to long leg, BG/AB = BE/BG, and since BE = BC,
we can use BG for the side s.

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