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A2

Part of 2004 Putnam

Problems(1)

Putnam 2004 A2

Source:

12/11/2004
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?
Putnamgeometryfunctiontrigonometryarea of a triangleHeron's formulacollege contests