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

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

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26 Sep 2018, 02:47
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Difficulty:

25% (medium)

Question Stats:

72% (01:06) correct 28% (01:23) wrong based on 46 sessions

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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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Director
Joined: 20 Feb 2015
Posts: 793
Concentration: Strategy, General Management
In the figure below, AD = 3. What is the length of AC?  [#permalink]

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26 Sep 2018, 03:01
1
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
CEO
Joined: 12 Sep 2015
Posts: 3020
Re: In the figure below, AD = 3. What is the length of AC?  [#permalink]

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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.

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

Now focus on the red 30-60-90 triangle

Here, side AB is opposite the 30° angle, and side AB has length 6
So, the hypotenuse AC must have length 12

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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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