Resistance of a wire is directly proportional to its length and inversely proportional to square of its radius
So, Resistance, $R \propto \frac{l}{r^2}$
$R = k \frac{l}{r^2}$, where $k$ is some constant.
Say $R_1,l_1,\;and\;r_1$ are Resistance, length and radius for first wire, similarly $R_2,l_2,\;and\;r_2$ for second wire
Given, $\frac{r_1}{r_2}= \frac{9}{8}$ and $l_1=162$cm
And, both wire having same resistance,
So, $R_1=R_2$
$k\frac{l_1}{r_1^2}=k\frac{l_2}{r_2^2}$
$l_2= l_1\left(\frac{r_2}{r_1} \right )^2 =162\times \left( \frac{8}{9}\right) ^2$
$128cm$
