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Parallelepiped Chimney

The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60 inches, and the height of the lower side of the lintel above the plane of the floor is 40 inches.  What is the length of the longest inflexible stick that can be put up this chimney?

The Mathematical Correspondent, Volume 1, 1804

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"Parallelepiped Chimney," Convergence (March 2006)