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A rectangle is to be inscribed in an isosceles right triangle in such a way...

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A rectangle is to be inscribed in an isosceles right triangle in such a way that one vertex of the rectangle is the intersection point of the legs of the triangle and the opposite vertex lies on the hypotenuse. Find the largest area (in cm) of the rectangle and its dimensions (in cm) given that the two equal legs of the triangle have length 6.

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