Legs of a right angle triangle are perpendicular and base.
The length of a parpendicular is 4 and the length of the base is considered 8.
By Pythagoras theorem,
[tex]\begin{gathered} H^2=P^2+B^2 \\ H^2=4^2+8^2 \\ H^2=16+64^{} \\ H^2=80 \\ H=4\sqrt[]{5} \end{gathered}[/tex]Hence, the correct option is (B)