The Parallelogram with Maximum Perimeter for Given Diagonals Is the Rhombus—A Proof Without Words and a Corollary

Abstract

SummaryBy the Law of Cosines and the arithmetic mean-root mean square inequality it is proved without words that The Parallelogram with Maximum Perimeter for given Diagonals is the Rhombus. As a corollary it also proved that for two positive numbers, their arithmetic mean is greater or equal than the arithmetic mean of their geometric mean and their root mean square.