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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Sandy
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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.

Thank you.

Sorry folks.
I have edited the original answer choices.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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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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