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What is the area of triangle ABC shown above?

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What is the area of triangle ABC shown above? [#permalink] New post 01 Jun 2016, 16:48
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77% (00:57) correct 22% (00:58) wrong based on 22 sessions
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What is the area of triangle ABC shown above?

A. 18

B. 20

C. \(12\sqrt{3}\)

D. \(18\sqrt{3}\)

E. 36

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[Reveal] Spoiler: OA

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Re: What is the area of triangle ABC shown above? [#permalink] New post 01 Jun 2016, 16:52
Expert's post
Explanation

The triangle is a 30°-60°-90° triangle, so the ratio of the lengths of the legs is 1 to \(\sqrt{3}\). Since the
length of the shorter leg, AB, is 6, it follows that the length of the longer leg, AC, is \(\frac{6}{3}\). The area
of the triangle is therefore \(\frac{1}{2}6*6\sqrt{3}\), or \(18\sqrt{3}\).

The correct answer is Choice D.
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Re: What is the area of triangle ABC shown above? [#permalink] New post 05 Jul 2017, 20:00
sandy wrote:
Explanation

The triangle is a 30°-60°-90° triangle, so the ratio of the lengths of the legs is 1 to \(\sqrt{3}\). Since the
length of the shorter leg, AB, is 6, it follows that the length of the longer leg, AC, is \(\frac{6}{3}\). The area
of the triangle is therefore \(\frac{1}{2}6*6\sqrt{3}\), or \(18\sqrt{3}\).

The correct answer is Choice D.


How come 18\sqrt{3} will be equal to 18/3?
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Re: What is the area of triangle ABC shown above? [#permalink] New post 05 Jul 2017, 20:26
Hi
The choices mentioned are wrong..

I took 4 minutes and 40 seconds and could not get my head around the choices until I saw your solution which mentions that D is correct..

Correct the typos and please make sure that there are no typos at-least in the question part.

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Re: What is the area of triangle ABC shown above? [#permalink] New post 26 Jul 2017, 00:30
Doesn't D say 18/3 than 18/root 3? Please check the symbols - I picked A cause that was the closes to 18*root3
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Re: What is the area of triangle ABC shown above? [#permalink] New post 11 Feb 2019, 10:49
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Sorry folks.
I have edited the original answer choices.

Cheers,
Brent
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Re: What is the area of triangle ABC shown above? [#permalink] New post 28 May 2019, 10:17
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Im having trouble indentifying 6/3 for length AC. How are we getting that? Is it due to the enlargement ratio being 6. can someone please elaborate???


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Re: What is the area of triangle ABC shown above? [#permalink] New post 28 May 2019, 11:23
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Forget the explanations above.

The triangle is a \(30:60:90\) triangle

Now it adheres to the standard \(x:x \sqrt{3}: 2x\)

Now the opposite side to the smallest angle - 30 - is 6.

So the standard above becomes \(6 : 6 \sqrt{3}: 12\) because \(x = 6\)

So the area is \(\frac{b*h}{2} = \frac{6 \sqrt{3} * 6}{2} = \frac{36 \sqrt{3} }{2} = 18 \sqrt{3}\)

D is the answer.

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Re: What is the area of triangle ABC shown above?   [#permalink] 28 May 2019, 11:23
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