I have three values which I want to express in ratios.
$l = 176.43$
$m = 162.86$
$n = 190$
The ratios must be:
$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} $
How to find $a$, $b$ and $c$? I tried so hard, but I couldn't find the values because they are not independents.
Is there some method?, or is it enough with algebra?
On
In this kind of situation, a good principle is to name the object.
Suppose that
$$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} .$$
Call this quantity $\lambda$.
You have
$$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c}=\lambda$$ and if $\lambda \neq 0$ (which is the case if none of $l,m,n$ is equal to zero), you get
$$a = \frac{l}{\lambda}, \, b = \frac{m}{\lambda}, \, c = \frac{n}{\lambda}.$$
Conversely, it is easy to verify that such $a,b,c$ are solutions.
We have found all possible solutions.
Let the common ratio be $\dfrac{1}{k}$. Remember $k$ should not be $0$.
$\dfrac{l}{a} = \dfrac{m}{b} = \dfrac{n}{c} = \dfrac{1}{k} $
Thus we get $a=lk$, $b=mk$, $c=nk$. Now just put the values of $l,m,n$