Geometry · Herons formula · Am gm inequality · Isoperimetric problem · Triangle area · Tangent lengths
Problem 4, 2006
Prove that among all triangles with one and the same perimeter, the equilateral triangle has the largest area.
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Serbian Republic Competition (Republicko takmicenje) 2006, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source