\(d+d'=160\)
\(\dfrac{d'}{d}=9\Rightarrow d'-9d=0\)
\(\left\{{}\begin{matrix}d+d'=160\\d'-9d=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}d'=144\left(cm\right)\\d=16\left(cm\right)\end{matrix}\right.\)
\(f=\dfrac{dd'}{d+d'}=\dfrac{144.16}{144+16}=14,4\left(cm\right)\)