Anti-Pythagoras

Geometry Level 3

In a picture such as a triangle above, we know that the areas \(c^2 + b^2 = a^2\).

However, imagine a triangle with non-zero area and sides \(a,b,c\) where \(c\) is the longest, with squares extended outwards from each side, each with a side length of that triangle. In what cases is the sum of the perimeters of the squares \(a\) and \(b\) greater than the perimeter of square \(c\)?

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