MathDB

S <= 1/5 A, A is sum of distinct product of sides of convex pentagon

Source: 2011 Belarus TST 4.1

November 7, 2020

geometrypentagongeometric inequality

Problem Statement

Let

A

be the sum of all

10

distinct products of the sides of a convex pentagon,

S

be the area of the pentagon. a) Prove thas

S \le \frac15 A

. b) Does there exist a constant

c<\frac15

such that

S \le cA

?
I.Voronovich