Beatrix decorates the faces of a cube, whose edges have length 2. For each face, she either leaves it blank, or draws a single straight line on it. Every line drawn joins the midpoints of two edges, either opposite or adjacent, as shown.
What is the exact length of the longest unbroken line that Beatrix can draw on the cube?
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100\text{km}
80\text{km}
50\sqrt{2}\text{km}
60\text{km}
33\frac{1}{3}\text{km}
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