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What is the area of triangle ABC shown above? [#permalink]
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 Practice Questions Question: 7 Page: 101
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Re: What is the area of triangle ABC shown above? [#permalink]
01 Jun 2016, 16:52
ExplanationThe 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]
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]
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 atleast in the question part.
Thank you.



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Re: What is the area of triangle ABC shown above? [#permalink]
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 Thank you



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Re: What is the area of triangle ABC shown above? [#permalink]
11 Feb 2019, 10:49
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]
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???
Thank you.



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Re: What is the area of triangle ABC shown above? [#permalink]
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. Regards
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Re: What is the area of triangle ABC shown above?
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