# 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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