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# In the figure above, what is the length of LO ?

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Math Expert
Joined: 02 Sep 2009
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In the figure above, what is the length of LO ?  [#permalink]

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04 Feb 2018, 20:10
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15% (low)

Question Stats:

95% (01:23) correct 5% (01:02) wrong based on 55 sessions

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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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2018-02-05_0809.png [ 10.48 KiB | Viewed 671 times ]

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Re: In the figure above, what is the length of LO ?  [#permalink]

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04 Feb 2018, 20:21
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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Re: In the figure above, what is the length of LO ?  [#permalink]

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05 Feb 2018, 08:29
uighelani wrote:
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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Re: In the figure above, what is the length of LO ?  [#permalink]

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05 Feb 2018, 08:38
Chakolate wrote:
uighelani wrote:
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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Re: In the figure above, what is the length of LO ?  [#permalink]

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05 Feb 2018, 13:19
Bunuel wrote:
Chakolate wrote:
uighelani wrote:
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 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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Re: In the figure above, what is the length of LO ?  [#permalink]

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05 Feb 2018, 21:44
Chakolate wrote:
Bunuel wrote:
Chakolate wrote:
[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 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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Re: In the figure above, what is the length of LO ?  [#permalink]

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06 Feb 2018, 08:02
uighelani wrote:
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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Re: In the figure above, what is the length of LO ?  [#permalink]

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06 Feb 2018, 08:10
Chakolate wrote:
uighelani wrote:
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.

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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Re: In the figure above, what is the length of LO ?   [#permalink] 06 Feb 2018, 08:10
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