GATE CSE 2015 Set 2 | Question: GA-7

Question

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 $\text{km}$?

• A. $5.34$
• B. $6.74$
• C. $28.5$
• D. $45.49$

Comments

I understood the solution to this problem but I am unable to figure out why can we not take point O from the middle of MN i.e OP will be parallel to MN and half the distance of MN? Am i missing out on anything?

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@chokostar it is given that N is southeast of O by 1km

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i think here some explanation should also need to add like angle NOP = 45 . so that the

sin45 = perpendicular / hypotanouse

= > perpendicular i.e. a= 1/root 2                    

 and also

cos45 = base / hypotanouee

= > base . = 1/root 2                

so that  required distance to get solution is  ( 2-  1/root 2)

Answer 1

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

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

Solving we get $x = 5.34.$ 

Correct Answer: $A$

Comments

#sid edit the comment .... nthing is showing ....

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again showing same dont know whats the problem  preview is correct

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How do we get a = 1/sqrt(2)

someone please tell me

Answer 2

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

Comments

this explaination is for me.

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Just unlocked a different dimension

Answer 3

Explanation: 

Answer 4

For anything unclear, feel free to comment/message.

Hence, Option A

Comments

MB should be 2 right?

Because MB+BN+NK =4

NK = 2-(1/√2 )

BN = 1/√2

then MB+1/√2+2-(1/√2 )=4

both (1/√2 )will be cancelled and then MB+2 =4 will be there

And then MB =2 but how could u take MB= 4-1/√2