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Freddy has a piece of string that is 20 inches long. He wants to use t

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Freddy has a piece of string that is 20 inches long. He wants to use t [#permalink]

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New post 01 May 2017, 10:10
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Freddy has a piece of string that is 20 inches long. He wants to use the string as the perimeter of a rectangle. What is the greatest area that rectangle could have?

A. 5
B. 10
C. 20
D. 25
E. 40
[Reveal] Spoiler: OA

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Re: Freddy has a piece of string that is 20 inches long. He wants to use t [#permalink]

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New post 01 May 2017, 10:34
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SajjadAhmad wrote:
Freddy has a piece of string that is 20 inches long. He wants to use the string as the perimeter of a rectangle. What is the greatest area that rectangle could have?

A. 5
B. 10
C. 20
D. 25
E. 40


For all the rectangles with a given area the rectangle with all 4 sides equal (Square) will have the maximum area
So, Perimeter of square = 4a = 20 => a = 5
Area = a*a = 5*5=25
Answer D
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Re: Freddy has a piece of string that is 20 inches long. He wants to use t [#permalink]

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New post 20 Aug 2017, 04:30
We can use elimination and addition here:
e - 40 : 2*20 here total of sides is 40+4 so not possible/ 8*5 total of sides 16 plus 10 exceeds 20/ 4*10 total 28 total so 40 ruled out
d- 25 --> 5*5 = 25 -- total of side 20; can keep
a,bc, too small in terms of total of sides
Ans D

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Re: Freddy has a piece of string that is 20 inches long. He wants to use t [#permalink]

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New post 06 Dec 2017, 13:35
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Hi All,

We're asked to use a 20 inch string to form the perimeter of a rectangle. We're asked for the LARGEST possible rectangular area that could be created. This question is built around a relatively rare concept (while you might see it on Test Day, it would likely be just once). In simple terms, when dealing with a 'fixed' total length as described in the prompt, the largest area will be created when you form a SQUARE.

For example, with a 20 inch string, you could form the following rectangles:
A 1x9 rectangle with an area of 9
A 2x8 rectangle with an area of 16
A 3x7 rectangle with an area of 22
A 4x6 rectangle with an area of 24
A 5x5 rectangle with an area of 25

There's no other possible rectangle that will lead to an area that is larger than 25.

Final Answer:
[Reveal] Spoiler:
D


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Re: Freddy has a piece of string that is 20 inches long. He wants to use t   [#permalink] 06 Dec 2017, 13:35
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