Question

If $p:q:r=1:2:3then$ $\sqrt{5p^2+q^2+r^2}$ is equal to:

• A. 4r
• B. 5p
• C. 2q
• D. 5

Answer 1

The correct option is B 5p

Consider the problem

Given, $p:q:r=1:2:3$

Therefore, $\frac{p}{1}=\frac{q}{2}=\frac{r}{4}=k$ (let)

So, $p=k,q=2k,r=4k$

Therefore,

$\begin{array}{c}\sqrt{5p^2+q^2+r^2}\\ =\sqrt{5k^2+4k^2+16k^2}\\ =\sqrt{25k^2}\\ 5k=5p\end{array}$

Hence, Option $B$ is the correct answer which is $5p$