Boxed In

Geometry Level 3

A square with side \(1\) falls on top of an open top square box with side \(1\) (pictured above). Assuming the square doesn't fall completely in the box, find the smallest value for \(x\), where \(x\) is the the line that connects the vertex of the square inside the box to the box base perpendicularly.

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Michael Fuller by Michael Fuller
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