Question

if (a+b):(b+c):(c+a)= 6:7:8 and (a+b+c)=14 then the value of c

Answer 1

let (a + b) = 6k
     (b + c) = 7k
     (c + a) = 8k 
where k is proportionality constant .
           now, add all equations 
(a + b) + (b + c) + ( c + a) = 6k + 7k + 8k = 21k
2(a + b + c) = 21k
                         a/c to question,
(a + b + c ) = 14 , put it above 
   then, 2 * 14 = 21k
 k = 4/3 
hence, (a + b) = 6k = 6*4/3 = 8
  now, c = (a + b + c) - (a + b)
              = 14 - 8 = 6 
hence, c = 6