Answer
Please see the work below.
Work Step by Step
We know that
$W=mg=\frac{GmM}{r^2}$
Thus, the weight is inversely proportional to $r^2$
$\implies \frac{W_{planet}}{W_{Earth}}=(\frac{r_{Earth}}{r_{planet}})^2$
This can be rearranged as:
$r_{planet}=\sqrt{\frac{W_{Earth}}{W_{planet}}}r_{Earth}$
$\implies r_{planet}=\sqrt{\frac{1}{2}}r_{Earth}$
We plug in the known values to obtain:
$r_{planet}=(0.7071)(6370Km)$
$r_{planet}=4500Km$
