# Triangle Theory

Geometry Level 5

Let $$S$$ be a set of 5 distinct integers {a, b, c, d, e} such that any subset of size 3 derived from this set can be possible sides for a scalene oblique triangle, and that for any 3 elements chosen, the GCD is 1.

Let $$Q$$ be the set of the areas of the triangles whose sides correspond to the elements of the subsets derived from set $$S$$.

Determine the minimum value of the sum of the square of the elements of $$Q$$.

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