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a,b,c and pa,qb,rc triangles with equal areas

Source: Czech-Polish-Slovak Match 2003

March 18, 2007
geometryalgebra proposedalgebra

Problem Statement

Numbers p,q,rp,q,r lies in the interval (25,52)(\frac{2}{5},\frac{5}{2}) nad satisfy pqr=1pqr=1. Prove that there exist two triangles of the same area, one with the sides a,b,ca,b,c and the other with the sides pa,qb,rcpa,qb,rc.
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