Breaking stress of a steel wire is p and the density of steel is ρ...

Maximum stress $= \dfrac{Maximumweight}{Cross - sectionalarea}$

Now, maximum weight of steel wire

= Volume $\times$ Density $\times g= Alρg$

where, $l$ is the maximum length of steel wire that can hang vertically without breaking. $ρ$ is the density of steel and $A$ is the cross-sectional area of steel wire.
$∴$ Maximum stress, $p = \dfrac{Alρg}{A} = lρg$

$∴ l = \dfrac{p}{ρg}$