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Updated on: 07 Aug 2018, 06:59
Originally posted by EgmatQuantExpert on 08 Nov 2016, 05:13.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:59, edited 2 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 06:59, edited 2 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:17) correct
41%
(02:31)
wrong
based on 286
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Rectangle DEFG is inscribed in an equilateral triangle as shown above. What is the area of triangle ABC?
- (1) The area of rectangle DEFG is 8√3 square units
(2) The area of triangle AGD is 2√3 square units
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16 Dec 2016, 11:08
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Solution
Hey,
Please find below the official solution.
So, expressing all the unknown lengths in terms of x and y, we get:
Note:
From the above diagram, we can infer that –
Thus, in order to find the area of the triangle, we need to know the value of x and y.
Analyze Statement 1 independently
Therefore statement 1 is not sufficient to arrive at a unique answer.
Analyze Statement 2 independently
Thus, we can write -
Therefore, statement 2 is not sufficient to arrive at a unique answer.
Analyze by combining statement 1 and 2
Therefore both statement 1 and 2 are required to answer the question.
Hence the correct Answer is C
Thanks,
Saquib
Quant Expert
e-GMAT
Hey,
Please find below the official solution.
- • We are given that \(ABC\) is an equilateral triangle.
- o This means, each angle of this triangle is \(60^o\).
• Also, \(DEFG\) is a rectangle.
- o Hence each angle of this rectangle is \(90^o\).
• Since the opposite sides of a rectangle are parallel, \(DE || GF\), and therefore, \(DE || AB\).
- o So, \(∠ CDE = ∠ CAB = 60^o\) (corresponding angles)
o Similarly, \(∠ CED = ∠ CBA = 60^o\).
- • Now, let’s assume that side \(GF = x\) units and side \(GD = y\) units.
So, expressing all the unknown lengths in terms of x and y, we get:
Note:
• Since Triangle \(AGD\) is a \(30^o-60^o-90^o\) triangle, the ratio of the sides are \(AG : DG : AD = 1 : √3 : 2\)
• Thus if \(DG = y\), then \(AG = y/√3\) and \(AD = 2y/√3\)
• And we can conclude the same for the sides of triangle \(EFB\).
From the above diagram, we can infer that –
- • The Sides of an equilateral triangle \(ABC = x+2y/√3\)
Thus, in order to find the area of the triangle, we need to know the value of x and y.
Analyze Statement 1 independently
- • The area of rectangle \(DEFG\) is \(8√3\) square units
- o That is, \(xy = 8√3\) . . . (1)
o Multiple values of x and y will satisfy this equation.
Therefore statement 1 is not sufficient to arrive at a unique answer.
Analyze Statement 2 independently
- • The area of triangle \(AGD\) is \(2√3\) square units
Thus, we can write -
- • \(1/2*AG*GD=2√3\)
• \(1/2*y/√(3 )*y=2√3\)
• \(y^2=2^2×3\)
• \(y=2√3\) . . . (2)
• But we don’t know the value of x yet.
Therefore, statement 2 is not sufficient to arrive at a unique answer.
Analyze by combining statement 1 and 2
- • Put the value of y from equation (2) in equation (1) and we will get: \(x = 4\)
• Since we now know the value of x and y, we can find the area of triangle.
Therefore both statement 1 and 2 are required to answer the question.
Hence the correct Answer is C
Thanks,
Saquib
Quant Expert
e-GMAT
General Discussion
