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In the figure below, AD = 3. What is the length of AC?

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Manager
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Joined: 01 Feb 2018
Posts: 92
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In the figure below, AD = 3. What is the length of AC?  [#permalink]

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New post 26 Sep 2018, 02:47
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E

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Question Stats:

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In the figure below, AD = 3. What is the length of AC?
A. 3
B. \(3\sqrt{3}\)
C. 6
D. \(6\sqrt{2}\)
E. 12

Please refer to the image attached

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In the figure below, AD = 3. What is the length of AC?  [#permalink]

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New post 26 Sep 2018, 03:01
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Sreyoshi007 wrote:
In the figure below, AD = 3. What is the length of AC?
A. 3
B. \(3\sqrt{3}\)
C. 6
D. \(6\sqrt{2}\)
E. 12

Please refer to the image attached


BDA is a rt triangle with angles 30:60:90 and therefore the sides will be in the ratio
1:\(\sqrt{3}\):2
1p=3
p=3
BA = 6 and
BD = 3\(\sqrt{3}\)

similarly triangle DBC is a rt triangle with angles 30:60:90
where
BD = 3\(\sqrt{3}\)
DC = \(\sqrt{3}\) * 3\(\sqrt{3}\) = 9
AC = DC + AD = 12
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Joined: 12 Sep 2015
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Re: In the figure below, AD = 3. What is the length of AC?  [#permalink]

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New post 19 Oct 2018, 08:26
Top Contributor
Sreyoshi007 wrote:
In the figure below, AD = 3. What is the length of AC?
A. 3
B. \(3\sqrt{3}\)
C. 6
D. \(6\sqrt{2}\)
E. 12

Please refer to the image attached


Key Concept: In a 30-60-90 triangle, the hypotenuse is twice the length of the side opposite the 30° angle.
Image


Side AD is opposite the 30° angle
Since AD = 3, the hypotenuse AB must have length 6
Image


Now focus on the red 30-60-90 triangle
Image
Here, side AB is opposite the 30° angle, and side AB has length 6
So, the hypotenuse AC must have length 12

Answer: E

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Re: In the figure below, AD = 3. What is the length of AC? &nbs [#permalink] 19 Oct 2018, 08:26
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In the figure below, AD = 3. What is the length of AC?

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