278. 
A wooden cube, whose edges are one centimeter long, rests on a horizontal surface. Illuminated by a point source of light that is centimeters directly above an upper vertex, the cube casts a shadow on the horizontal surface. The area of a shadow, which does not include the area beneath the cube is 48 square centimeters. Find the greatest integer that does not exceed . This problem is copyrighted by the American Mathematics Competitions.

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