If p : q : r = 1 : 2 : 4, then 5p^2 + q^2 + r^2 is equal to -

Answer: Option C

$$\begin{array}{rl}& p=k,q=2k,r=4k\\ & \text{Then,}\\ & \sqrt{5p^2+q^2+r^2}\\ & =\sqrt{5k^2+{\left(2k\right)}^2+{\left(4k\right)}^2}\\ & =\sqrt{5k^2+4k^2+16k^2}\\ & =\sqrt{25k^2}\\ & =5k\\ & =5p.\end{array}$$