Question

$P$ is $300$ km eastward of $O$ and $Q$ is $400$ km south of $O$. $R$ is exactly in the middle of $Q$ and $P$. The distance between $Q$ and $R$ is __ km.

• A. $500$
• B. $250$
• C. $250\sqrt{2}$
• D. $300$

Answer 1

The correct option is B $250$

Given,
$P$ is $300$ Km Eastward to $O$
$Q$ is $400$Km South to $O$
$R$ is Middle in $Q$ and$P$

$\because O{P}^2+O{Q}^2=Q{P}^2$
$\therefore QP=\sqrt{(300{)}^2+(400{)}^2}=\sqrt{90000+160000}$
$\Rightarrow \sqrt{250000}$
$QP=500$
$\therefore QP=\frac{QP}{2}$
$\Rightarrow \frac{500}{2}=250$
Hence, option 'B' is correct.