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What is the maximum possible area of a parallelogram with on

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What is the maximum possible area of a parallelogram with on [#permalink]

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What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters?

Last edited by Bunuel on 20 Sep 2013, 16:23, edited 1 time in total.
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What is the maximum possible area of a parallelogram with on [#permalink]

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jlgdr wrote:
What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters?


The perimeter = 2*2 + 2x = 24 --> x = 10.

The area is maximized if the parallelogram is a rectangle, thus the maximum area is 2*10 = 20.
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Re: What is the maximum possible area of a parallelogram with on [#permalink]

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Re: What is the maximum possible area of a parallelogram with on [#permalink]

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New post 07 May 2015, 00:36
Bunuel wrote:
jlgdr wrote:
What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters?


The perimeter = 2*2 + 2x = 24 --> x = 10.

The are is maximized if the parallelogram is a rectangle, thus the maximum area is 2*10 = 20.


Dear Bunuel:

In this question I have one query that as per the Theory learnt - Max. possible Area with a given perimeter is a SQUARE, so why here it is RECTANGLE?
Pls help with an explanation.

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Re: What is the maximum possible area of a parallelogram with on [#permalink]

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anu1706 wrote:
Bunuel wrote:
jlgdr wrote:
What is the maximum possible area of a parallelogram with one side of length 2 meters and a perimeter of 24 meters?


The perimeter = 2*2 + 2x = 24 --> x = 10.

The are is maximized if the parallelogram is a rectangle, thus the maximum area is 2*10 = 20.


Dear Bunuel:

In this question I have one query that as per the Theory learnt - Max. possible Area with a given perimeter is a SQUARE, so why here it is RECTANGLE?
Pls help with an explanation.


Hi anu1706

You are right in your understanding that the maximum possible area for a given perimeter is a square.
So for a give perimeter of 24, the sides should have been 24/4 = 6 units each.

But here we have an additional constraint that the length of one of the sides is 2.
Now, if the other sides are also 2 each, the perimeter will only be 8 and not 24.

So the only way to have a perimeter of 24 and length of one of the sides as 2 is to take the parallelogram as a rectangle, which will result in the answer explained in the posts above.

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Re: What is the maximum possible area of a parallelogram with on [#permalink]

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New post 07 May 2015, 03:00
Hi anu1706

You are right in your understanding that the maximum possible area for a given perimeter is a square.
So for a give perimeter of 24, the sides should have been 24/4 = 6 units each.

But here we have an additional constraint that the length of one of the sides is 2.
Now, if the other sides are also 2 each, the perimeter will only be 8 and not 24.

So the only way to have a perimeter of 24 and length of one of the sides as 2 is to take the parallelogram as a rectangle, which will result in the answer explained in the posts above.[/quote]

Thanks!! I got it now..

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Re: What is the maximum possible area of a parallelogram with on   [#permalink] 07 May 2015, 03:00
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