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Minimizing Perimeter (Posted on 2015-03-04) Difficulty: 2 of 5
Let ABC be a triangle with integral side lengths such that angle A=3 * angle B. Find the minimum value of its perimeter.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts NO DICE.....not a spoiler | Comment 1 of 15

imho there is no triangle with integer sides  such that

 angle B=3 * angle A,  A being the smallest.

The function   f= sinA+SIN(3A)+SIN(4A)  has
a  minimum   (or maybe maximum*)  value when

A=0.577969  radians 
and the closest to an "integer " triplet 

is    20, 27, 36.12 

 i.e. a perimeter   slightly over  83.

*min or max - ............I  have solved f'=0



Please comment, hope I DID NOT ERR

Edited on March 4, 2015, 8:57 am
  Posted by Ady TZIDON on 2015-03-04 08:54:07

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