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Perimeter ratio

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by arellalu » Thu Aug 09, 2012 3:52 pm
The perimeters of Square 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 area of region S?

a) 25:26

b) 24:25

c) 5:6

d) 4:5

e) 4:9
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by GMATGuruNY » Thu Aug 09, 2012 5:37 pm
arellalu wrote:The perimeters of Square 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 area of region S?

a) 25:26

b) 24:25

c) 5:6

d) 4:5

e) 4:9
Since Square S has 4 equal sides, plug in values for Rectangle R that yield a perimeter divisible by 4.

Rectangle R:
Let b=4 and h=6.
P = 2(4+6)=20.
A = 4*6 = 24.

Square S:
Since S has the same perimeter as R, P = 20.
Thus, s = 20/4 = 5.
A = 5² = 25.

R/S = 24/25.

The correct answer is B.
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by cypherskull » Tue Aug 14, 2012 1:55 pm
Since the sides of the rectangle is given to be in the ratio of 2:3, I guess the area (LxB) has to be a multiple of 6 (2x3).

The only option is B.
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