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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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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need more info that is width for rectangle

Ans D

Could we experiment for choice B in the square case (each side 7)? " since the square is a form a rectangle or no? "

Yes, it would be valid to test a 7x7 square since squares are types of rectangles.
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square side is 24/4=6, thus area is 36

length and width of the rectangle can be anything from just a little more than 7 length and just a little less than 7 width for an area of almost 49. thus bigger than square.
But, it can be also, a width of 1, length of 13 with area of 13, thus less than square.

Answer D)The relationship cannot be determined from the information given.
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