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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 re(2): NO DICE.....not a spoiler | Comment 6 of 15 |
(In reply to re: NO DICE.....not a spoiler by Jer)

I still do not know where did I  err.

Please comment on my reasoning:

The perimeter i.e. a+b+c= 2r*(sina+sin3a+sin4a)

IF I ASSUME R=1  then the function that matters is

f=(sina+sin3a+sin4a) and f'=cosa+3cos3a+cos4a

I found the angle for which f'=0  ,it was slightly over 33 degrees.

evaluating sina, sin3a and  sin4a  I got  a ratio a:b:c   which

is like 20:27:36  but not quite.

Maybe, choosing R as a constant, and limiting   my   solution to

only one family of congruent triangles was the cause of my erring.

I still would welcome an analytical solution or at least some  guidance.

  Posted by Ady TZIDON on 2015-03-04 11:40:57
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