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rectangles with area at least 4, rom sel tests

Source: Romanian ROM TST 2004, problem 2, created by Dan Ismailescu

May 1, 2004
geometryrectangleinequalitiesanalytic geometrygeometry proposed

Problem Statement

Let {Ri}1≤i≤n\{R_i\}_{1\leq i\leq n} be a family of disjoint closed rectangular surfaces with total area 4 such that their projections of the OxOx axis is an interval. Prove that there exist a triangle with vertices in ⋃i=1nRi\displaystyle \bigcup_{i=1}^n R_i which has an area of at least 1. [Thanks Grobber for the correction]
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