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29 Oct 2020, 00:15
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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:
55%
(hard)
Question Stats:
65% (02:30) correct
35%
(02:23)
wrong
based on 104
sessions
History
Date
Time
Result
Not Attempted Yet
In the given figure ABCD is a rectangle and EF || AD. AEG and FEB are two triangles inscribed in the rectangle ABCD such that the area of triangle AEG is half of the area of triangle FEB. What is the area of rectangle ABCD?
(1) EBCF is a square of side length 5 centimeters.
(2) A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halves
Attachment:
1.jpg [ 7.61 KiB | Viewed 7024 times ]
prashant0099
Joined: 25 Jan 2016
Last visit: 20 Dec 2020
Posts: 47
Given Kudos: 65
Location: India
Schools: Alberta '23
GPA: 3.9
WE:Engineering (Energy)
29 Oct 2020, 00:38
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given area AEG= 1/2 area of aeg
hence 1/2 * AE* EG =1/2 * 1/2 * EB* EF
from 1 we know EB and EF are 5 but still we dont know how much is length of AE so NS
from (2)
A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halves
As the line passing through G divides the rectangle into 2 equal halves,
So, EG = GF
but no length is given hence alone is not sufficient.
combining,
we know AE =5
hence Area of rectangle ABCD = 25 + 5*5 = 50 cm
Sufficient hence C
hence 1/2 * AE* EG =1/2 * 1/2 * EB* EF
from 1 we know EB and EF are 5 but still we dont know how much is length of AE so NS
from (2)
A line passing through point G and parallel to AB divides the rectangle ABCD into 2 equal halves
As the line passing through G divides the rectangle into 2 equal halves,
So, EG = GF
but no length is given hence alone is not sufficient.
combining,
we know AE =5
hence Area of rectangle ABCD = 25 + 5*5 = 50 cm
Sufficient hence C
Bunuel
29 Oct 2020, 01:08
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According to the information given in the question stem, EF is perpendicular to AB (EF || AD), and \(AE * GE = 2 * EF * EB\) ( the area of triangle AEG is half of the area of triangle FEB ). Now to further calculate the area of the rectangle ABCD, I would like to know the product of length and breadth of the rectangle. Let me assume, breadth CB = AD = x, and length AB = CD = y.
1) According to first statement, EB = EF = x = 5.
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * EG = 2 * 5^2\)
Since we do not know the measure of AE and EG, this information is insufficient.
2) According to second statement, EF = CB = x, but EG = \(1/2\).x
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * 1/2 * x = 2 * x * EB\)
Solving this, I get AE = 4 EB. Furthermore, y = AE + EB = 5 EB.
But we do not have the value of EB.
Thus, this information is also insufficient, since it only helps us getting values in ratios and variables.
Combining both information in 1 and 2, I can find the answer to the question. In (1) we got EB = x = 5, and in (2) we got y = 5 EB, so y = 25. Therefore, option C is the correct answer.
1) According to first statement, EB = EF = x = 5.
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * EG = 2 * 5^2\)
Since we do not know the measure of AE and EG, this information is insufficient.
2) According to second statement, EF = CB = x, but EG = \(1/2\).x
So, \(AE * GE = 2 * EF * EB\) can be written as \(AE * 1/2 * x = 2 * x * EB\)
Solving this, I get AE = 4 EB. Furthermore, y = AE + EB = 5 EB.
But we do not have the value of EB.
Thus, this information is also insufficient, since it only helps us getting values in ratios and variables.
Combining both information in 1 and 2, I can find the answer to the question. In (1) we got EB = x = 5, and in (2) we got y = 5 EB, so y = 25. Therefore, option C is the correct answer.
