The given expression can be expressed as, cot 2A : cot 2B : cot 2C = 4 : 3 : 2 …… (1) (s−b)(s−c)s(s−a) : (s−b)(s−c)s(s−a) : (s−b)(s−c)s(s−a) = 4 : 3 : 2 Multiply the above equation with (s−a)(s−b)(s−c). (s−a):(s−b):(s−c)=4:3:22a+b+c−a:2a+b+c−b:2a+b+c−c=4:3:2 …… (2) From equation (1) and equation (2), b+c−a=4ka+c−b=3ka+b−c=2k Solve the above equation. Then, a=25kb=26kc=27k The ratio of a:b:c is calculated as, a:b:c=5:6:7