Let ABC be a triangle with integral side lengths such that angle A=3 * angle B. Find the minimum value of its perimeter.

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