MathDB

A bound on side length

Source: Tournament of Towns, Fall 2002, Senior A Level, P2

May 17, 2014

geometry3D geometryinequalitiesgeometry proposed

Problem Statement

A cube is cut by a plane such that the cross section is a pentagon. Show there is a side of the pentagon of length

\ell

such that the inequality holds:

|\ell-1|>\frac{1}{5}