GATE CSE 2015 | Set 2 | GA | Question: 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

please explain

 

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Is there any way to solve this question without using sin45?

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Let the point of intersection of ON and MP be Q.
 

Triangles OQP and NQM are similar triangles (O ~ N, P~M)

Thus, OQ= 1/3 Km and QN=2/3 Km (by ratios)
 

In triangle OQN , we have OP=2 , OQ=1/3 and and angle(POQ) = 45 degrees
 

By cosine property, OP= rootof(4+1/9 -4/(3*sqrt(2)) = 1.78
 

thus MP= PQ+QM= 3*1.78=5.34

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

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

someone please tell me

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for understanding @Praveen Saini's comment (the $1^{st}$ one)

the triangle inequality theorem states:

• The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
• The difference between the lengths of any two sides must be less than the length of the remaining side.

Hence, for a right angle triangle, $a + b > c > a - b$ Where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides. This means the hypotenuse is always less than the sum of the other two sides, but greater than their difference.

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reason why a=1/root(2)

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

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@skeltro nice and concise answer.

Answer 3

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

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@Srken MN = 4 and MK $\neq$ 4, MK = $4 + 2 - \frac{1}{\sqrt{2}}$ = $6 - \frac{1}{\sqrt{2}}$

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@JashanArora nice and detailed answer.

Answer 4

Explanation: 

Answer 5

answer is a 5.34

Comments

explain pls?

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Explanation please!!!!!!!!

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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

Answer 6

Just giving more details to Accepted answer.