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# What is the minimum possible perimeter of a quadrilateral

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Current Student
Joined: 06 Sep 2013
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20 Sep 2013, 16:11
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What is the minimum possible perimeter of a quadrilateral with an area of 1,600 square feet?
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16 Apr 2015, 19:22
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Hi all,

Even if you don't know the 'secret' to this question, you can still figure out the correct answer by 'playing around' with the possibilities a bit.

We're given a quadrilateral with an area of 1600. Working with the simplest quadrilaterals (rectangles/squares) will make this work pretty easy...

IF....
Length = 1, Width = 1600
Area = 1600
Perimeter = 2(1600) + 2(1) = 3202

IF...
Length = 10, Width = 160
Area = 1600
Perimeter = 2(160) + 2(10) = 340

Notice in these two examples that when we make the length and width "closer" to one another, the perimeter DECREASES.... A few more examples will pinpoint the MINIMUM perimeter....

IF...
Length = 20, Width = 80
Area = 1600
Perimeter = 2(80) + 2(20) = 200

IF...
Length = 40, Width = 40
Area = 1600
Perimeter = 2(40) + 2(40) = 160

There's no smaller perimeter than 160, since increasing the length beyond 40 will force us to decrease the width under 40 (and we already can see from the prior examples what that does to the perimeter.

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20 Sep 2013, 16:29
jlgdr wrote:
What is the minimum possible perimeter of a quadrilateral with an area of 1,600 square feet?

For a given area the perimeter will be minimized for a square --> side^2=1,600 --> side = 40 --> the perimeter = 4*40 = 160.
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16 Apr 2015, 18:06
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Re: What is the minimum possible perimeter of a quadrilateral   [#permalink] 16 Apr 2015, 18:06
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