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Triangle in a Square

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Triangle in a Square

A triangle is placed on the interior of a square so that two of the triangle's vertices lie on two adjacent vertices of the square, and the third vertex lies on the opposite side,
1
3
of the way between the two endpoints.

If the perimeter of the triangle (in linear units) is equal to the area of the triangle (in square units), what is the length of the side of the square?

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Problem by BogusBoy

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