A basic problem about Thales's theorem

Question

We have a $\triangle ABC$. Points $M, N$ lie on $AC$ and $BC$, respectively as $MN$ $||$ $AB$. $BC=14$ $cm$, $CM=2$ $cm$ and $AM=5$ $cm$. I should find the length of $CN$.

I am having trouble with a simple geometry problem that uses Thales's theorem. $MN$ $||$ $AB$ if and only if $\dfrac{CM}{CN}=\dfrac{AM}{BN}$. Did I get the ratio right?

Answer 1

Yes, your ratio is correctly calculated. Now mark $CN = x$ then $BN = 14-x$ and finsih the job.

Answer 2

That is correct. It would be more straightforward to say that $\frac{CM}{AC}=\frac{CN}{BC}$, which leads you to $\frac2{2+5}=\frac x{14}$