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# If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim

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Joined: 08 Jul 2010
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If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim  [#permalink]

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18 Nov 2017, 05:33
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65% (hard)

Question Stats:

52% (01:30) correct 48% (02:01) wrong based on 53 sessions

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If the Perimeter of Quadrilateral ABCD is P then find P?

1) The maximum possible area of a quadrilateral with perimeter P is 36
2) Maximum Possible area of a triangle with Perimeter P is 16√3

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Re: If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim  [#permalink]

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18 Nov 2017, 05:42
GMATinsight wrote:
If the Perimeter of Quadrilateral ABCD is P then find P?

1) The maximum possible area of a quadrilateral with perimeter P is 36
2) Maximum Possible area of a triangle with Perimeter P is 16√3

Source: http://www.GMATinsight.com

1. Maximum possible area of Quad is a^2 (Area of Square).
2. Maximum possible area of Traingle is root(3)/4 * a^2 (Area of Equilateral Triangle).

So, D.
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Re: If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim  [#permalink]

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27 Nov 2017, 23:34
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To be able to solve this question, we should know that:

For all quadrilaterals with a given perimeter, Square has Maximum area
For all triangles with a given perimeter, Equilateral Triangle has Maximum area
Basically, for a polygon of n sides, with a fixed perimeter, it will have Maximum area if its a Regular polygon (all sides and all angles equal)

Now over to the question

(1) Since this says Max possible area is 36, it means this quadrilateral is a square. Square will have area as side^2.
side^2 = 36 or side = 6. So side of this quadrilateral is 6, hence Perimeter P = 4*6 = 24. Sufficient

(2) Same logic, this will be an equilateral triangle. Area of equilateral triangle with side a = √3/4 * a^2, this is 16√3
Solving we get a=8, hence Perimeter P = 3*8 = 24. Sufficient.

Re: If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim &nbs [#permalink] 27 Nov 2017, 23:34
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# If the Perimeter of Quadrilateral ABCD is P then find P? 1) The maxim

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