One of the best ways to motivate little kids to learn math (n = 2 admittedly) is to present it as secrets for cheating.
And their sum is half the perimeter of that same rectangle. But this is geometrically rather unnatural. The Babylonians found a better way.
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They took two copies of the rectangle, rotated one by 90 degrees, and juxtaposed them to make a shape whose base is the sum of the sides.
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But this shape is unappealingly asymmetrical. So they made a second copy of it, rotated it by 180 degrees, and assembled both into a square.
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