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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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A triangle that works, may not be minimum | Comment 4 of 15 |
I decided to see what would happen if sin(B)=3/5.
sin(A)=sin(3B)=117/125
sin(C)=sin(180-4B)=sin(4B)=336/625
by the law of sines
14000a=21840b=24375c
and the minimum integer solution to this is 
a=195, b=125, c=112
for a perimeter of 432.

I don't know if this is a minimum.  I haven't even tried sin(B)=4/5.

  Posted by Jer on 2015-03-04 09:47:08
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