The Triangle of Minimum Perimeter Nov 2025

I got curious 🤔

I present the problem and my solution.

Conclusion

For a triangle with a given base and altitude, an isosceles triangle has the minimum perimeter.
At x=0.0, P'(x) = -\dfrac{1}{\sqrt{1+Y^{2}}}
At x=0.5, P'(x) = 0
At x=1.0, P'(x) = +\dfrac{1}{\sqrt{1+Y^{2}}}


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