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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How come 18\sqrt{3} will be equal to 18/3?

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.

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

Sorry folks.
I have edited the original answer choices.

Cheers,
Brent
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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.

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

Recognizing that this is a \(30:60:90\) triangle, we know the legs will be in the ratio:

\(x:x \sqrt{3}: 2x\), where the hypotenuse is 2x


So, the two legs are \(6\) and \(6\sqrt{3}\). This is all the information we need to find the area.


Area = \(\frac{b*h}{2}\)
= \((6*6\sqrt{3})/2\)
= \((36\sqrt{3})/2\)
= \(18\sqrt{3}\)

Answer is D.

The trick here is that the 30-60-90 triangle is presented in the no-so-common orientation.

Therefore, x = 6 and x.root(3) = 6.root(3)

Base = 6.root(3)

Height = 6

Area = 1/2 x Base x Height

Area = 1/2 x 6.root(3) x 6 = 18.root(3)

Area = 18.root(3)

Answer is D
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