What is the value of $k$, if $\frac{(a+b)}{c}=\frac{(b+c)}{a}=\frac{(c+a)}{b}=k$.
Given: $\frac{(a+b)}{c}=\frac{(b+c)}{a}=\frac{(c+a)}{b}=k$
To do: To find the value of $k$.
Solution:
$\because \frac{(a+b)}{c}=\frac{(b+c)}{a}=\frac{(c+a)}{b}=k$
$\Rightarrow a+b=ck\ ----( 1)$
$\Rightarrow b+c=ak\ ----( 2)$
$\Rightarrow c+a=bk\ ----( 3)$
On adding $( 1),\ ( 2)$ and $( 3)$
$a+b+b+c+c+a=ck+ak+bk$
$\Rightarrow 2a+2b+2c=k( a+b+c)$
$\Rightarrow 2( a+b+c)=k( a+b+c)$
$\Rightarrow k=2$
Hence, $k=2$
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