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Four branches of a company are located at $\text{M, N, O}$ and $\text{P. M}$ is north of $\text{N}$ at a distance of $4\;\text{km; P}$ is south of $\text{O}$ at a distance of $2\;\text{km; N}$ is southeast of $\text{O}$ by $1\;\text{km}$. What is the distance between $\text{M}$ and $\text{P}$ in $\text{km}$?

1. $5.34$
2. $6.74$
3. $28.5$
4. $45.49$

use scale for such type of question :P
Actually a good idea if you get stuck somewhere.
Haha ,, scale is not allowed

$a=\dfrac{1}{\sqrt{2}}$

$x=\sqrt{[4+(2-a)]^{2}+a^2}$

Solving we get $x = 5.34.$

Correct Answer: $A$

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#sid edit the comment .... nthing is showing ....
again showing same dont know whats the problem  preview is correct
How do we get a = 1/sqrt(2)

For those who didn't understand previous explanations....

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### 1 comment

this explaination is for me.
Explanation:

explain pls?
south

first draw diagm according to the question keeping directions w.r.t west....| ...east

north

then draw perpendicular from point N to line OP. after that use sin 45  to find length of perpendicular . then apply pythago. theorem to find one part of OP add 4 to remaining part of OP to get 5.34 as ans