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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: $A$

by

Well here as I noticed that we don't need to calculate it as perpendicular is 4+2-(1/sqrt2) and base is 1/sqrt 2,  hypotenuse should be less than perpendicular + base. So it should be less than 6. Only option left is 5.34.
@Arjun , Please give more clear & Detailed explanation for this question.  I've spent good amount of time on this ( I remember discussing with you this question. I did not get it yet !
best way to get it clear, take a graph paper( or assume) . keep O at origin  (or any).  mark x- axis as east, y-axis as north, opposite of x-axis as west and  opposite of y-axis as south. follow the language of question.
@Arjun how did u get a=1/2^0.5 i m getting a=2^0.5
ON makes a 45 degrees with MN(as it points to south-east), and measures 1 kilometer. using trigonometric ratio , a can be calculated as  a=1 x cos (45)
@Arjun sir, why you took the a part of OP as $a$. Please explain why $a = 1/\sqrt(2)$
South West - means angle is 45 degrees. So, right angled isosceles triangle.
Someone plz fix it ... its N ...nt Z ...
edited by
$ON= 1 = \sqrt { \left ( 1/\sqrt{2} \right )^{2}+\left ( 1/\sqrt{2} \right )^{2}}$
#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)

someone please tell me

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

by

### 1 comment

this explaination is for me.
Explanation:
answer is a 5.34

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