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 \(Q\).

×

Problem Loading...

Note Loading...

Set Loading...