If AD is 6, and ADC is a right angle, what is the area of

Question

https://www.manhattangmat.com/images/triangleABC/triangleABC.jpg If AD is 6, and ADC is a right angle, what is the area of triangular region ABC? (1) Angle ABD = 60° (2) AC = 12 OPEN DISCUSSION OF THIS QUESTION IS HERE: if-ad-is-6-and-adc-is-a-right-angle-what-is-the-area-of-101200.html

MackyCee · Answer

No matter what I do, I keep getting to "D" - can anyone help me out?

Info from the given:
Based on my understanding of ADC being right, the triangle MUST be isosceles, and triangles ABD and ADC are similar triangles. Is this correct??

Reasoning:
1) Knowing the given of the question, and we know that if angle ABD is 60 degrees => triangle is equilateral, and both triangles are similar triangles (both 30-60-90 triangles).

Knowing the "ratios" of a 30-60-90 triangle, and the dimensions of AD, we can find the value of ANY of the other sides, and hence the area. Sufficient

2) Knowing AD and AC, we can find DC by Pythagoras Theorem, and knowing triangles are similar, we can find the total area. Sufficient.

Can anyone lead me to "C", the OA? Or is the OA wrong?

Sudhanshuacharya · Answer

Macky: If the triangle is right angled that does not mean that the triangle is isosceles. I could have been assumed as isosceles only if AD was also bisecting the angle A.

From statement 1 we can only find length of BD. Not sufficient
From statement 2 we can find only the length of DC. Hence not sufficient.

Combining both we get the height and the total base of the triangle, from which we can deduce the area.

MackyCee · Answer

Musta been the time of night - but you are definitely 100% correct (as is MGMAT), it doesn't have to be isosceles at all, I must have had my head n the clouds with another concept :S

I need a holiday! haha

suraabhi · Answer

Hey,

I also did the mistake but I think MGMAT is right. But this is typical DS question which tricks you with mixed information.

(1) From first you only see one rt angle triangle on the left hand side is 30-60-90 but still do not know anything on the right hand side rt angle triangle

(2) From this statement you know only one side of the base. The point D is not the midpoint. Hence you do know know the lenght of whole base.

(1) & (2) You know the lenght of whole base BD + DC and you have the height given.

Hence C is the right answer.
Please correct me if i am wrong :-)

subhajeet · Answer

A realiy tough question. I too made the same mistake...

kudos to MGMAT.

shinna · Answer

C is the answer, that was tough! whew! :shock:

dsmishra1981 · Answer

C is the answer. It was easy guys, pretty straight forward.

When nothing is given about the figure, one should take only the info that is present in the question.

unceldolan · Answer

I don't see how C can be right. If I follow your reasoning, I come to E. (I chose B)

Can anyone explain the calculations?

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=17129 If AD is 6 and ADC is a right angle, what is the area of triangular region ABC? Given: AD=6 . Question: area_{ABC}=\frac{1}{2}*AD*BC=\frac{1}{2}*6*(BD+DC)=3(BD+DC)=? (1) Angle ABD = 60 --> triangle ABD is 30-60-90 triangle, so the sides are in ratio 1:\sqrt{3}:2 --> as AD=6 (larger leg opposite 60 degrees angle) then BD=\frac{6}{\sqrt{3}} (smallest leg opposite 30 degrees angle). But we still don't know DC. Not sufficient. (2) AC=12, we can find DC. But we still don't know BD. Not sufficient. (1)+(2) We know both BD and DC, hence we can find area. Sufficient. Answer: C. OPEN DISCUSSION OF THIS QUESTION IS HERE: if-ad-is-6-and-adc-is-a-right-angle-what-is-the-area-of-101200.html

If AD is 6, and ADC is a right angle, what is the area of

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