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 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.**