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

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

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New post Updated on: 16 Dec 2018, 06:58
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In ΔJKL shown above, what is the length of segment JL?

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

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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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New post 09 Dec 2014, 07:03
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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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New post 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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New post 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.


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

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New post 26 Dec 2014, 09:59
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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New post 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
Correct Answer - D
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Re: In ΔJKL shown above, what is the length of segment JL?  [#permalink]

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