Practice: Find The Distance Between The Skew Lines

Geometry Level 5

The base of a pyramid ABCSABCS is an equilateral triangle ABCABC with a side length of 42.4\sqrt{2}. The edge SCSC is perpendicular to the base and has length 2.2. Let DD and EE be the midpoints of ABAB and BCBC respectively. The (shortest) distance between the skew lines SESE and CDCD can be written as ab,\sqrt{\frac{a}{b}}, where aa and bb are coprime positive integers. Find a+b.a+b.

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