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Sub 505 (Easy)|   Geometry|      
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In the figure above, what is the length of LO ? 04 Feb 2018, 21:10
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In the figure above, what is the length of LO ?


(A) 2

(B) \(2\sqrt{2}\)

(C) \(2\sqrt{3}\)

(D) 4

(E) \(4\sqrt{2}\)

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In the figure above, what is the length of LO ? 04 Feb 2018, 21:21
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Knowing that triangle KJN is right triangle with two sides = 1, we know that the hypotenuse is Square root of 2.
Since it is given that KN = KL = LM = MN, we know all sides are equal to sq. root 2.
Knowing LM is = sq. root 2 and it is a 30, 60, 90 triangle, we can conclude LO is 2√2, or answer choice B
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In the figure above, what is the length of LO ? 05 Feb 2018, 09:29
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uighelani
Knowing that triangle KJN is right triangle with two sides = 1, we know that the hypotenuse is Square root of 2.
Since it is given that KN = KL = LM = MN, we know all sides are equal to sq. root 2.
Knowing LM is = sq. root 2 and it is a 30, 60, 90 triangle, we can conclude LO is 2√2, or answer choice B
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How do you know that it's a right triangle?
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In the figure above, what is the length of LO ? 05 Feb 2018, 09:38
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Chakolate
uighelani
Knowing that triangle KJN is right triangle with two sides = 1, we know that the hypotenuse is Square root of 2.
Since it is given that KN = KL = LM = MN, we know all sides are equal to sq. root 2.
Knowing LM is = sq. root 2 and it is a 30, 60, 90 triangle, we can conclude LO is 2√2, or answer choice B

How do you know that it's a right triangle?
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That sign indicates that angle J is 90 degrees.
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In the figure above, what is the length of LO ? 05 Feb 2018, 14:19
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Bunuel
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uighelani
Knowing that triangle KJN is right triangle with two sides = 1, we know that the hypotenuse is Square root of 2.
Since it is given that KN = KL = LM = MN, we know all sides are equal to sq. root 2.
Knowing LM is = sq. root 2 and it is a 30, 60, 90 triangle, we can conclude LO is 2√2, or answer choice B

How do you know that it's a right triangle?

That sign indicates that angle J is 90 degrees.
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That tells you that KJN is right, not that LMO is. Or am I looking too hard for the trick? On the GMAT it's hard to tell just how suspicious one should be. :-)
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In the figure above, what is the length of LO ? 05 Feb 2018, 22:44
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Chakolate
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[quote="uighelani"]Knowing that triangle KJN is right triangle with two sides = 1, we know that the hypotenuse is Square root of 2.
Since it is given that KN = KL = LM = MN, we know all sides are equal to sq. root 2.
Knowing LM is = sq. root 2 and it is a 30, 60, 90 triangle, we can conclude LO is 2√2, or answer choice B

How do you know that it's a right triangle?

That sign indicates that angle J is 90 degrees.

That tells you that KJN is right, not that LMO is. Or am I looking too hard for the trick? On the GMAT it's hard to tell just how suspicious one should be. :-)[/quote]

Because it is given KN = KL = LM = MN, meaning it’s a squares. So each interior angle = 90 degrees and therefore the corresponding exterior angle is also 90 degrees, making LMO a 30, 60 90 triangle.


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In the figure above, what is the length of LO ? 06 Feb 2018, 09:02
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uighelani

Because it is given KN = KL = LM = MN, meaning it’s a squares. So each interior angle = 90 degrees and therefore the corresponding exterior angle is also 90 degrees, making LMO a 30, 60 90 triangle.
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No, KN=KL=LM=MN means it's a rhombus, not necessarily a square. This may just be overly esoteric, since 'no way to tell' isn't one of the possible answers. It just seems a little sloppy to me.
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In the figure above, what is the length of LO ? 06 Feb 2018, 09:10
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Chakolate
uighelani

Because it is given KN = KL = LM = MN, meaning it’s a squares. So each interior angle = 90 degrees and therefore the corresponding exterior angle is also 90 degrees, making LMO a 30, 60 90 triangle.

No, KN=KL=LM=MN means it's a rhombus, not necessarily a square. This may just be overly esoteric, since 'no way to tell' isn't one of the possible answers. It just seems a little sloppy to me.
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Sure - but a Rhombus with equals sides still means it has equal angles. (Regular)

If you want to really be detailed, plug it into the polygonal angle formula and divide by 4.

180(N-2) where N is the number of sides. 180(2) = 360. 360/4 = 90.


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