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04 May 2021, 03:00
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A
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Question Stats:
53% (02:17) correct
47%
(01:58)
wrong
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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
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
08 May 2021, 00:45
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Bunuel
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.
Attachment:
Triangle.png [ 10.74 KiB | Viewed 2907 times ]
