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What is the area of an obtuse angled triangle whose two sides are 8 an

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Bunuel
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What is the area of an obtuse angled triangle whose two sides are 8 an [#permalink] New post   04 May 2021, 03:00
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What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?


A. 24 square units

B. 48 square units

C. \(24*\sqrt 3\) square units

D. \(48*\sqrt 3\) square units

E. Such a triangle does not exist
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Re: What is the area of an obtuse angled triangle whose two sides are 8 an [#permalink] New post   04 May 2021, 03:03
Option A right? 0.5*4*12 = 24sq units
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Re: What is the area of an obtuse angled triangle whose two sides are 8 an [#permalink] New post   08 May 2021, 00:45
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Bunuel wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?


A. 24 square units

B. 48 square units

C. \(24*\sqrt 3\) square units

D. \(48*\sqrt 3\) square units

E. Such a triangle does not exist


Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:



Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

For more check Triangles chapter of Math Book: https://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

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Triangle.png
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Re: What is the area of an obtuse angled triangle whose two sides are 8 an [#permalink] New post   08 May 2021, 00:50
Bunuel wrote:
Bunuel wrote:
What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?


A. 24 square units

B. 48 square units

C. \(24*\sqrt 3\) square units

D. \(48*\sqrt 3\) square units

E. Such a triangle does not exist


Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:



Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

For more check Triangles chapter of Math Book: https://gmatclub.com/forum/math-triangles-87197.html

Hope it helps.

Show Spoiler
Attachment:
Triangle.png



Area of triangle when two sides and it's included Angle is given would be

1/2* a*b*sin( included Angle )

Hence 1/2*8*12*1/2 = 24

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Re: What is the area of an obtuse angled triangle whose two sides are 8 an [#permalink]
08 May 2021, 00:50
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