MathDB

Problem 2 of Third round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022

algebra

Problem Statement

We say that a rectangle and a triangle are similar, if they have the same area and the same perimeter. Let

P

be a rectangle for which the ratio of the longer to the shorter side is at least

\lambda -1+\sqrt{\lambda (\lambda -2)}

where

\lambda =\frac{3\sqrt{3}}{2}

. Prove that there exists a tringle that is similar to

P