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

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

edited | 4.8k views
+8
use scale for such type of question :P
0
Actually a good idea if you get stuck somewhere.
+1
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 Veteran (431k points)
edited
+4
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.
+4
@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 !
+5
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.
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@Arjun how did u get a=1/2^0.5 i m getting a=2^0.5
+1
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)
+1
@Arjun sir, why you took the a part of OP as $a$. Please explain why $a = 1/\sqrt(2)$
+3
South West - means angle is 45 degrees. So, right angled isosceles triangle.
+1
Someone plz fix it ... its N ...nt Z ...
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$ON= 1 = \sqrt \left ( 1/\sqrt{2} \right )^{2}+\left ( 1/\sqrt{2} \right )^{2}$
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#sid edit the comment .... nthing is showing ....
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again showing same dont know whats the problem  preview is correct
0
How do we get a = 1/sqrt(2)

For those who didn't understand previous explanations.... by (353 points)
+1
this explaination is for me.
+1 vote
by Active (1.4k points)
+1
explain pls?
0
0
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

For anything unclear, feel free to comment/message.    Hence, Option A

by Loyal (6.6k points)
Explanation: by Active (1.2k points)

Just giving more details to Accepted answer. by (429 points)