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Show that 36S ≤ L^2 √3, where S is area and L is perimeter

Source:

May 22, 2011
geometryperimetercircumcircleinequalitiesarea of a triangle

Problem Statement

The area of a triangle is SS and the sum of the lengths of its sides is LL. Prove that 36S≤L2336S \leq L^2\sqrt 3 and give a necessary and sufficient condition for equality.
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