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

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sm0k3rz
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If AD is 6, and ADC is a right angle, what is the area of [#permalink] New post   01 Jun 2010, 05:22
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A
B
C
D
E

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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



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C
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mc
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Re: If AD is 6, and ADC is a right angle, what is the area of [#permalink] New post   01 Jun 2010, 05:37
Since we know the height (AD), we only need to find the base length (BC)

i: ABD = 60, but we don't know BAC or ACD, so we can only find the length of BD, not BC, which we need.
ii: Again, we can find the length of DC, but not BC.

Combined: Since we can find BD from (i), and DC from (ii), we have BC and can find the area. Answer is C.
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Re: If AD is 6, and ADC is a right angle, what is the area of [#permalink] New post   03 Jun 2010, 18:30
guys please post OA.

Don't forget some one else will be waiting for answer :peek
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Re: If AD is 6, and ADC is a right angle, what is the area of [#permalink] New post   11 Aug 2017, 02:40
Expert Reply
sm0k3rz wrote:

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



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



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Re: If AD is 6, and ADC is a right angle, what is the area of [#permalink]
11 Aug 2017, 02:40
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