MathDB

Triangle sidelengths

Source: RMO 2004, Grade 7, Problem 2

February 26, 2006

inequalities

Problem Statement

The sidelengths of a triangle are

a,b,c

. (a) Prove that there is a triangle which has the sidelengths

\sqrt a,\sqrt b,\sqrt c

. (b) Prove that

\displaystyle \sqrt{ab}+\sqrt{bc}+\sqrt{ca} \leq a+b+c < 2 \sqrt{ab} + 2 \sqrt{bc} + 2 \sqrt{ca}