This page uses JavaSketchpad. You may drag any of the red points, and the construction will adjust accordingly.

Explanation of the construction: If the original square has side s and the double-area square has side t, then we need t^2 = 2s^2, or t = sqrt(2)s. By the Pythagorean Theorem, the diagonal of the original square is sqrt(2)s, so we just use construction 4 with the diagonal as the given side.

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