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Perimeters (GMAT Prep)

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Perimeters (GMAT Prep)

by alex.gellatly » Sat Jun 30, 2012 3:05 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 area of region S?

25:16
24:25
5:6
4:6
4:9
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by Anurag@Gurome » Sat Jun 30, 2012 3:17 am
alex.gellatly 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 area of region S?
Say, lengths of the sides of R are 2a and 3a.
Hence, area of R = (2a)*(3a) = 6a²

Perimeter of R = 2(2a + 3a) = 10a = perimeter of S
Length of each side of S = 10a/4 = 5a/2
Hence, area of S = (5a/2)*(5a/2) = 25a²/4

Therefore, required ratio = 6a²/(25a²/4) = 24/25

The correct answer is B.
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by GMATGuruNY » Sat Jun 30, 2012 4:22 am
alex.gellatly 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 area of region S?

25:16
24:25
5:6
4:6
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 sandeep_thaparianz » Sat Jun 30, 2012 5:06 am
+1 for B
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