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# In ΔJKL shown above, what is the length of segment JL?

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Math Expert
Joined: 02 Sep 2009
Posts: 52231
In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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Updated on: 16 Dec 2018, 06:58
00:00

Difficulty:

5% (low)

Question Stats:

88% (00:24) correct 12% (00:39) wrong based on 122 sessions

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Project DS Butler: Day 41: Data Sufficiency (DS82)

In ΔJKL shown above, what is the length of segment JL?

(1) JK = 10
(2) KL = 5

Kudos for a correct solution.

Attachment:

2014-12-09_1826.png [ 2.75 KiB | Viewed 6149 times ]

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Originally posted by Bunuel on 09 Dec 2014, 06:27.
Last edited by gmatbusters on 16 Dec 2018, 06:58, edited 1 time in total.
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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09 Dec 2014, 07:03
1
In ΔJKL shown above, what is the length of segment JL?

(1) JK = 10

First off, we should recognize right away that angle L measures 90 degrees since the three angles of any triangle add up to 180 degrees. Now that we know the triangle is a 30-60-90 degree right triangle, we only need the length of any one side to figure out the length of any of the other sides. We are told segment JK = 10, so we can figure out that JL would equal 5*sqrt(3) using the properties of 30-60-90 degree right triangles.

(2) KL = 5

We can apply the same logic that we applied in Statement 1 using the information we receive in Statement 2. Again, it is imperative to recognize that angle L measures 90 degrees. We are given that segment KL = 5, so using the properties of a 30-60-90 degree right triangle, we can see that segment JL measures 5*sqrt(3) units.

Each statement alone is sufficient to answer the question. Answer is D.
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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09 Dec 2014, 09:31
In ΔJKL shown above, what is the length of segment JL?

As this is a 30-60-90 triangle, knowing any one side will enable us to calculate the lengths of the other two sides in the ratio of 1:sqrt(3):2, respectively.

(1) JK = 10 Sufficient--we can calculate the lengths of any other side.
(2) KL = 5 Sufficient--we can calculate the lengths of any other side.

Choice D
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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10 Dec 2014, 02:40
1
ΔJKL is right angle triangle. What is the length of segment JL?
The length of legs in every 30-60-90 right angle triangle is in the ratio $$1:\sqrt{3}: 2$$
Or, KL : JL : JK = $$1:\sqrt{3}: 2$$

Statement (1)
JK = 10
$$\frac{{JL}}{{JK}}= \sqrt{3}/2$$

or, JL = $$5\sqrt{3}$$.......................................... sufficient.

Statement (2)
KL=5
$$\frac{{JL}}{{KL}}=\sqrt{3}$$

or, JL = $$5\sqrt{3}$$......................................... sufficient.

Math Expert
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Posts: 52231
Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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26 Dec 2014, 09:59
Bunuel wrote:

Tough and Tricky questions: Combinations.

In ΔJKL shown above, what is the length of segment JL?

(1) JK = 10
(2) KL = 5

Kudos for a correct solution.

Attachment:
2014-12-09_1826.png

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Location: United States (LA)
Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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04 Aug 2016, 13:52
The key to solving this question is determining that the given triangle is 30 - 60 - 90 right triangle
sides opposite to angles are in ratio of 1 :$$\sqrt{3}$$ : 2
Statement 1 gives us the length of side opposite to right angle
we can determine all 3 sides from this data so sufficient
Statement 2 gives us the length of side opposite to 30 deg angle
we can determine all 3 sides from this data so sufficient
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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17 Dec 2018, 16:47
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In ΔJKL shown above, what is the length of segment JL? &nbs [#permalink] 17 Dec 2018, 16:47
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