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Putnam 2004 A2

Source:

December 11, 2004
Putnamgeometryfunctiontrigonometryarea of a triangleHeron's formulacollege contests

Problem Statement

For i=1,2,i=1,2, let TiT_i be a triangle with side length ai,bi,ci,a_i,b_i,c_i, and area Ai.A_i. Suppose that a1≤a2,b1≤b2,c1≤c2,a_1\le a_2, b_1\le b_2, c_1\le c_2, and that T2T_2 is an acute triangle. Does it follow that A1≤A2A_1\le A_2?
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