Question

If (a+b): (b + c) : (c+a)= 6:7:
and (a + b + c) = 14, then the
value of c is :​

Answer 1

Answer :

The value of "c" is 6.

Explanation :

Correct Question :

If (a+b):(b+c):(c+a) = 6:7:8 and (a+b+c) = 14, what is the value of C?

Solution :

Given that :

(a + b +c) = 14

(a + b) = 6k

(b + c) = 7k

(c + a)=8k

Now,

Addition of LHS & RHS :

$\implies \sf 2a+2b+2c=21k\\\\\implies 2(a+b+c)=21k\\\\\implies 2(14) = 21k\\\\\implies 28=21k\\\\\implies k=\dfrac{28}{21}=\dfrac{4}{3}........Eq(1)$

As given :

(a + b + c) = 14

c = 14 - (a + b)

So,

$\sf \implies a+b=6k\\\\\sf \implies a+b=6 \dfrac{4}{3} \quad {From Eq(1)}\\\\\sf \implies a+b=8\\\\Now,\\\\\sf \implies c=14-(a+b)\\\\\sf \implies c=14- 8\\\\\sf \implies c=6$

Hence,

The value of 'C' = 6.