# Ratio and proportion?

• Jun 30th 2009, 10:49 PM
fardeen_gen
Ratio and proportion?
If we are given that:
$\frac{b + c - a}{1} = \frac{a + c - b}{2} = \frac{a + b - c}{3}$, how to find $a : b : c$?

(I was solving a trigonometry in triangles question, and I needed to find out $a:b:c$. I found that $\frac{s - a}{1} = \frac{s - b}{2} = \frac{s - c}{3}$, where s is semi-perimeter. Hence, the the given equation. On second thought, is there any way to find $a:b$ if we know $\frac{k + a}{k + b} = \lambda$, where k and $\lambda$ are known constants?)
• Jul 1st 2009, 12:19 AM
red_dog
$\frac{b+c-a}{1}=\frac{a+c-b}{2}=\frac{a+b-c}{3}=\frac{a+b+c}{6}=k$

$\left\{\begin{array}{ll}a+b+c=6k\\b+c-a=k\end{array}\right.\Rightarrow b+c=\frac{7k}{2}\Rightarrow a=\frac{5k}{2}$

In a similar way find b and c in term of k.