Question

If $(a+b):(b+c):(c+a)=6:7:8$ and $(a+b+c)=14$ , then the value of $c$ is

• A. $6$
• B. $7$
• C. $8$
• D. $14$

Answer 1

The correct option is A $6$

$a+b:b+c:c+a=6:7:8$

$a+b+c=14$

$\therefore \frac{a+b}{b+c}=\frac{6}{7}$ ……..$\left(1\right)$

$\therefore \frac{b+c}{c+a}=\frac{7}{8}$ ……..$\left(2\right)$

$\therefore \frac{a+b}{c+a}=\frac{6}{8}$ ...........$\left(3\right)$

From $\left(1\right)$ & $\left(2\right)$

$\begin{array}{cc}If& a+b=6x\\ then& b+c=7x\end{array}\}\to x\in R$

then $c+a=8x$

$\therefore 2(a+b+c)=6x+7x+8x$

$\therefore a+b+c=\frac{21x}{2}$

$\therefore a+b+c=10.5x$

$\therefore c=10.5x-6x$

$\therefore c=4.5x$

Also, $10.5x=14$

$\therefore x=\frac{14}{10.5}$

$\therefore c=\frac{4.5\times 14}{10.5}$

$\therefore c=6$.