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A vertical line divides a right triangle with base of length 1 and height of length 2 into two pieces. The figure below, with

A vertical line divides a right triangle with base of length 1 and height of length 2 into two pieces. The figure below, with the two shaded regions formed, illustrates how the vertical line can be placed at any percentage of the base. 0.65 Find the exact location of 2 (located between 0 and 1 on the base of the triangle) that maximizes the product of the two areas.

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