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- Jan 26, 2012

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Thanks again to those who participated in last week's POTW! Here's this week's problem!

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**Problem**: A rectangular box is to be inscribed in the tetrahedron whose faces are the coordinate planes and the plane $x/a+y/b+z/c=1$ (where $a$, $b$, and $c$ are positive constants). One corner of the box touches the plane, the opposite corner is at the origin, and the faces of the box are parallel to the coordinate planes. Find the dimensions of the largest such box.

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Remember to read the POTW submission guidelines to find out how to submit your answers!