3

Part of 1985 Austrian-Polish Competition

Problems(1)

Isoperimetric inequality revisited (for quadrilaterals)

Source: Austrian-Polish 1985, Problem 3

In a convex quadrilateral of area

1

, the sum of the lengths of all sides and diagonals is not less than

4+\sqrt 8

quadrilateralGeometric InequalitiesgeometryinequalitiesSumarea