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by candygal79 » Fri Apr 04, 2014 12:20 am
The perimeters of square regions and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
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by Brent@GMATPrepNow » Fri Apr 04, 2014 12:45 am
You made a small error in transcribing the question. I've fixed it below.
candygal79 wrote:The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Let's PLUG IN some values that meet the given conditions.

The sides of R are in the ratio 2:3
So, let the two sides have lengths 2 and 3.
This means the area of Region R = (2)(3) = 6
This means the ENTIRE perimeter of Region R is 2 + 2 + 3 + 3 = 10


The perimeters of square region S and rectangular region R are equal.
This means the perimeter of square region S is also 10
Since all 4 sides in a square are of equal length, each side must have length 2.5
So, the area of Region S = (2.5)(2.5) = 6.25

What is the ratio of the area of region R to the are of region S ?
We get: 6 : 6.25
Check the answer choices .... no matches. So, we need to take 6 : 6.25 and find an equivalent ratio.
If we multiply both parts by 4 we get: 24 : 25
So, the correct answer is B

Cheers,
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by GMATGuruNY » Fri Apr 04, 2014 2:11 am
The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Since a square has 4 equal sides, plug in multiples of 4.

Rectangle R:
Since L:W = 2:3, let L = 4*2 = 8 and W = 4*3 = 12.
Then:
Perimeter = L+W+L+W = 8+12+8+12 = 40.
Area = L*W = 8*12 = 96.

Square S:
Since S and R have the same perimeter, P = 40.
Since perimeter = 40, S=10.
Area = S² = 10² = 100.

Resulting ratio:
R/S = 96/100 = 48/50 = 24/25.

The correct answer is B.
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by Abhishek009 » Fri Apr 04, 2014 6:13 am
candygal79 wrote:The perimeters of square regions and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?

A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Let the sides of the Rectangle be 2 & 3

perimeter of the rectangle is 2 ( 2 + 3 ) => 10


Given -
The perimeters of square regions and rectangular region R are equal.
So , Perimeter of the square = 10

or, 4a = 10

Hence a = 10/4 => 2.5

So area of the square will be (2.5)^2 => 6.25

Area of the Rectangle will be 2*3 => 6.00
Ratio of the area of region R to the are of region S
Will be 600 / 625 => 120 / 125 => [spoiler]24 /25[/spoiler]

Hence answer will be definitely (B)
Abhishek
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