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27 Dec 2015, 10:42
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:39) correct
50%
(02:38)
wrong
based on 278
sessions
History
Date
Time
Result
Not Attempted Yet
What is the area of the triangle in the figure above?
A. \(2+2\sqrt{3}\)
B. \(4\sqrt{3}\)
C. 8
D. \(8\sqrt{3}\)
E. 12
Attachment:
2015-12-27_2141.png [ 9.56 KiB | Viewed 9586 times ]
29 Dec 2015, 00:47
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Bunuel
Hi,
the Q may be 700+, since you require to know to play around with Geometrical figures..
the best way is to look how we can draw a 90 degree angle , which will help us to break the figure down to simpler terms
[img]https://gmatclub.com/forum/download/file.php?mode=view&id=28776[/img]..
here we see the third angle C shouold be 45, so we draw a perpendicular from B to AC..
now we have two triangles ABD and BCD..
lets see the first triangle BCD..
angle BCD and CBD are 45 and CDB is 90...
\(Hyp = BC= 2\sqrt{2}\)...
so the sides BD and CD=2..
area of BCD=1/2 * 2*2=2...
lets see the second triangle ABD..
it is 30-60-90 triangle...
and therefore the sides BD:AD:AB are in ratio \(1:\sqrt{3}:2\)..
BD is 2, so AD = \(2\sqrt{3}\)..
so \(area = 1/2 * 2\sqrt{3}*2=2\sqrt{3}\)..
\(total Area=2+ 2\sqrt{3}\)
ans A
Attachments
ANGLES.png [ 24.18 KiB | Viewed 9194 times ]
General Discussion
01 Jan 2016, 12:11
Kudos
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Hi All,
Since the GMAT is built around existing patterns/rules/logic, the Geometry questions that you face on Test Day will almost always be based on standard shapes and formulas that you already know (or should know). Any time a question involves a shape that is 'weird', that shape can almost always be broken-down into smaller standard shapes - you can then use your knowledge of those shapes to answer the given question (although the math involved might be 'step-heavy').
Here, the weird shape is a 30/45/105 triangle. As chetan2u pointed out in his explanation, this triangle can be split into a 30/60/90 and a 45/45/90. From there, you can use the given side length, along with the rules for those 2 right triangles, to figure out ALL of the other side lengths and the total area of the shape.
GMAT assassins aren't born, they're made,
Rich
Since the GMAT is built around existing patterns/rules/logic, the Geometry questions that you face on Test Day will almost always be based on standard shapes and formulas that you already know (or should know). Any time a question involves a shape that is 'weird', that shape can almost always be broken-down into smaller standard shapes - you can then use your knowledge of those shapes to answer the given question (although the math involved might be 'step-heavy').
Here, the weird shape is a 30/45/105 triangle. As chetan2u pointed out in his explanation, this triangle can be split into a 30/60/90 and a 45/45/90. From there, you can use the given side length, along with the rules for those 2 right triangles, to figure out ALL of the other side lengths and the total area of the shape.
GMAT assassins aren't born, they're made,
Rich
