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# A quadrilateral has a perimeter of 16. Which of the following alone

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Joined: 12 Aug 2015
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Schools: Boston U '20 (M)
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A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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26 Mar 2017, 07:25
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57% (01:30) correct 43% (01:05) wrong based on 78 sessions

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A quadrilateral has a perimeter of 16. Which of the following alone would provide sufficient information to determine the area of the quadrilateral.

B)The quadrilateral is formed by combining two isosceles right triangles.

C) Two pairs of congruent angles are in a 2:1 ratio.

D) The width is 4o% of the length and all angles are of equal measure.

E) If the perimeter was decreased by 50%, the area would decrease by 25%.

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Joined: 17 Apr 2016
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Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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26 Mar 2017, 09:53
The answer has to be D.

The quadrilateral described in option D is a rectangle.
Reasons:-
1. All angles are equal.(Given) Hence each side is of 90 degree. So it has to be a square or a rectangle.
2. The width is 4o% of the length----> Implies it is not a square.---------------------------------------------------Equation (1)

We know the perimeter.

2(l +b)= 16.
l + b= 8.
Using equation 1, l and b can be calculated and the area will be = l * b.
Senior Manager
Joined: 06 Dec 2016
Posts: 250
Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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26 Mar 2017, 10:58
I think the answer is D
D is saying that the quadrilateral is a rectangle
Current Student
Joined: 12 Aug 2015
Posts: 2638
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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27 Apr 2017, 21:34
Intern
Joined: 27 Dec 2015
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Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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30 Apr 2017, 08:43
While I agree that D is accurate and leaves us with a rectangle, I initially picked B thinking that this would be a square (combining 2 45 45 90 triangles forming a square). So, I would also like to know why B is wrong if someone can explain.

Thanks!
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Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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30 Apr 2017, 11:47
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For Option B, the two diagrams are given below. According to me, since we can get two different type of quadrilateral, we cannot answer what would be the area with surety.

Thanks,
Saquib
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Re: A quadrilateral has a perimeter of 16. Which of the following alone  [#permalink]

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30 Apr 2017, 11:50
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Even in the case of Option C, we can get two different types of quadrilateral and hence the area would differ and with the limited information given, I don't think we can even find the area, with just the angles and sum of lengths.

Thanks,
Saquib
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Re: A quadrilateral has a perimeter of 16. Which of the following alone &nbs [#permalink] 30 Apr 2017, 11:50
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