MathDB
2012-2013 Winter OMO #44

Source:

January 16, 2013
Online Math Opengeometry3D geometrytetrahedroninequalitiesvectorincenter

Problem Statement

Suppose tetrahedron PABCPABC has volume 420420 and satisfies AB=13AB = 13, BC=14BC = 14, and CA=15CA = 15. The minimum possible surface area of PABCPABC can be written as m+nkm+n\sqrt{k}, where m,n,km,n,k are positive integers and kk is not divisible by the square of any prime. Compute m+n+km+n+k.
Ray Li
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