50

Part of 1970 IMO Longlists

Problems(1)

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

Source:

The area of a triangle is

S

and the sum of the lengths of its sides is

L

36S \leq L^2\sqrt 3

and give a necessary and sufficient condition for equality.

geometryperimetercircumcircleinequalitiesarea of a triangle