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The area of a square [#permalink]
26 Jun 2018, 09:12
Expert's post
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Question Stats:
85% (01:01) correct
14% (00:32) wrong based on 47 sessions
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Re: The area of a square [#permalink]
26 Jun 2018, 09:55
1
This post received KUDOS
Carcass wrote:
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
From Statement 1 we have
Perimeter of Square = 4 * side =24
or side = 6
Now area of square = \(6^2\) =36
From Statement 2;
Perimeter of rectangle = 2(Length * Breadth) = 28
or Length * Breadth = 14
Now suppose Length = 4 and breadth = 10
Then area of rectangle = Length * Breadth = 40 ; which is greater than Statement 1
But if Length = 2 and Breadth = 12
Then area of rectangle = Length * Breadth = 24 ; which is Less than Statement 1
Hence the option is D
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Re: The area of a square [#permalink]
30 Jun 2018, 06:56
1
This post received KUDOS
Expert's post
Carcass wrote:
Quantity A
Quantity B
The area of a square region with the perimeter of 24
The area of a rectangular region with the perimeter of 28
A)The quantity in Column A is greater. B)The quantity in Column B is greater. C)The two quantities are equal. D)The relationship cannot be determined from the information given.
Notice that Quantity A is FIXED. All sides of a square have the same length So, if the perimeter is 24, then each side has length 6 So, the area of the square = (base)(height) = (6)(6) = 36 So, QUANTITY A = 36
On the other hand, Quantity B can have infinitely many values Consider these two possible cases:
CASE A: if the perimeter of the rectangle is 28, then its dimensions could be 6 by 8 In this case, the area = (base)(height) = (6)(8) = 48 Since QUANTITY A = 36, we can see that Quantity B is greater
CASE B: if the perimeter of the rectangle is 28, then its dimensions could also be 1 by 13 In this case, the area = (base)(height) = (1)(13) = 13 Since QUANTITY A = 36, we can see that Quantity A is greater
Answer: D
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85% (01:01) correct
