Problem:
The rectangle is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is ?
Answer Choices:
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B.
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E.
Solution:
Let represent the end of the cut on , and let represent the end of the cut on . For a square to be formed, we must have
The rectangle that is formed by this cut is indeed a square, since the original rectangle has area , and the rectangle that is formed by this cut has a side of length .
The problems on this page are the property of the MAA's American Mathematics Competitions