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

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Joined: 19 Aug 2016
Posts: 84
If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

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16 Oct 2017, 01:46
zanaik89 wrote:

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.

Hi Bunuel

Cant we assume that that AD bisects BC into two?

So u mean that since it isnt given that triangle ABC is an isoceles triangle or equilateral triangle, we can not consider AD as a perpendicular bisector right?
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Joined: 02 Sep 2009
Posts: 51185
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

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16 Oct 2017, 01:53
zanaik89 wrote:

So u mean that since it isnt given that triangle ABC is an isoceles triangle or equilateral triangle, we can not consider AD as a perpendicular bisector right?

Yes, we know that AD is perpendicular to BC but we don't know whether it bisects BC.
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Re: If AD is 6 and ADC is a right angle, what is the area of triangular re  [#permalink]

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31 Aug 2018, 07:58
If AD is 6 and ADC is a right angle, what is the area of triangular region ABC?[/b]

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 the area. Sufficient.

Bunuel - My doubt is if a triangle like this which has a 30-60-90 angles, shouldn't the the triangle ADC should also be 30-60-90 making triangle ABC an equilateral triangle? because an equilateral triangle can be formed by joining two identical triangles, each with 30-60-90 angles.
Re: If AD is 6 and ADC is a right angle, what is the area of triangular re &nbs [#permalink] 31 Aug 2018, 07:58

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