If p : q : r = 1 : 2 : 4, then $$\sqrt {5{p^2} + {q^2} + {r^2}} $$     is equal to =

Solution (By Examveda Team)

$$\eqalign{ & {\text{p}}:{\text{q}}:{\text{r}} \cr & 1:2:4 \cr & x:2x:4x \cr & \therefore \sqrt {5{p^2} + {q^2} + {r^2}} \cr & = \sqrt {5{x^2} + 4{x^2} + 16{x^2}} \cr & = \sqrt {25{x^2}} \cr & = 5x \cr & = 5p \cr} $$