Let ABC be a triangle with integral side lengths such that angle A=3 * angle B. Find the minimum value of its perimeter.
(In reply to re: NO DICE.....not a spoiler
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.