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# The length of line segment AC

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The length of line segment AC [#permalink]  27 Jan 2016, 16:58
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Question Stats:

83% (00:55) correct 16% (01:21) wrong based on 36 sessions

 Quantity A Quantity B The length of line segmentAC 3

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 5
Page: 466
Difficulty: medium/hard
[Reveal] Spoiler: OA

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Kudos [?]: 1033 [1] , given: 4655

Re: The length of line segment AC [#permalink]  28 Jan 2016, 07:56
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Solution

If we name the height D, we do have a triangle $$BCD$$ in which we have the angles of 30-60-90 and $$ABD$$ 45-45-90.

From this, knowing the relative triplets $$x-x\sqrt{3}-2x$$ and $$x-x-\sqrt{2}$$

Now, $$BC =2$$ $$BD=\sqrt{3}$$ and $$DC=1$$. If $$BD =\sqrt{3}$$, $$AD$$ as well $$\sqrt{3}$$

So $$AC$$ is long $$\sqrt{3}+1$$ and is $$< 3$$

The answer is $$B$$
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Re: The length of line segment AC [#permalink]  07 Mar 2018, 09:50
x-x-sqrt(2) should be x-x-x*sqrt(2)
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Re: The length of line segment AC [#permalink]  11 Mar 2018, 07:14
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Re: The length of line segment AC [#permalink]  12 Mar 2018, 01:16
Re: The length of line segment AC   [#permalink] 12 Mar 2018, 01:16
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