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16 Oct 2017, 02:46
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zanaik89
Hi Bunuel
Cant we assume that that AD bisects BC into two?
Please clear my doubt thanks[/quote]
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?
16 Oct 2017, 02:53
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zanaik89
Yes, we know that AD is perpendicular to BC but we don't know whether it bisects BC.
31 Aug 2018, 08:58
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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.
Answer: C.
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.
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.
Answer: C.
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.
