The length of the largest altitude of the triangle formed by the lines $7\mathrm{x}-2\mathrm{y}+10=0$ ,  $7\mathrm{x}+2\mathrm{y}-10=0$and   $\mathrm{y}+2=0$is

It is the altitude to the least side length of largest altitude is the altitude to the least side.
  being smallest side $\left(\mathrm{i}.\mathrm{e}.\mathrm{y}+2=0\right)$

AC=4,$AB=\sqrt{53} ,AC=4,BC=\sqrt{53}$
$\therefore \mathcal{l}=\frac{\left|5+2\right|}{\sqrt{1}}=7$