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Optimize the Length of the Crease of a Folded Piece of Paper

​
distance x
2
A sheet of legal paper is 8.5 by 11.75 inches long. The lower-left corner is brought to a point
x
inches from the upper-left corner and folded to form a crease. This Demonstration shows a graph of the crease length as a function of
x
and a diagram of the folded paper. By moving the slider, you can estimate the length of the shortest and longest possible crease. The exact shortest possible crease (
51
3
8
≈11.04
) and the exact longest possible crease (
47
68
47
2
(47-9
13
)
≈12.78
) may be determined by using Mathematica or traditional calculus techniques.
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