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Cross Sections of a Cube

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Author: Annie Fetter
Description: Geometry, difficulty level 3. You have a cube whose surface area is 150 cm^2. What would be the perimeter of a square cross section of this cube? What is the perimeter of the largest rectangle you could get as a cross section? How could you get an equilateral triangle as a cross section?
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Problem page: http://mathforum.org/geopow/solutions/19971121.geopow.html
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