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Suppose that a right triangle has legs of lengths 3 cm and 2 cm. (Note that...

Suppose that a right triangle has legs of lengths 3 cm and 2 cm. (Note that the legs of a right triangle are the two sides that are not the hypotenuse.) A rectangle is inscribed in this right triangle so that two sides of the rectangle lie along the legs. Find the largest possible area of such a rectangle.
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