Anti-Pythagoras

Geometry Level 3

In a picture such as a triangle above, we know that the areas c2+b2=a2c^2 + b^2 = a^2.

However, imagine a triangle with non-zero area and sides a,b,ca,b,c where cc 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 aa and bb greater than the perimeter of square cc?

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