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square and rectangle

by joannabanana » Mon Oct 11, 2010 4:02 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?
a. 25:16
b. 24:25
c. 5:6
d. 4:5
e. 4:9

[spoiler]ans 24:25[/spoiler]
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by Rahul@gurome » Mon Oct 11, 2010 4:46 am
Let the sides of rectangle R be 2x and 3x. Then perimeter of R = 2*(2x + 3x) = 10x
So, each side of square S = 10x/4 = 5x/2
Area of R = (2x)(3x) = 6x^2
Area of S = (5x/2)^2 = 25x^2/4
Therefore, Area of R: Area of S = 6x^2 : 25x^2/4 = 24 : 25

[spoiler]The correct answer is (B).[/spoiler]
Last edited by Rahul@gurome on Mon Oct 11, 2010 4:47 am, edited 1 time in total.
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by Geva@EconomistGMAT » Mon Oct 11, 2010 4:46 am
Plug in numbers - the correct answer should hold for whatever number you pick, as long as they satisfy the requirements of the question.

Say that the sides of r are 4 and 6, so that the perimter of r is 2(4+6) = 20.
Square S has the same perimter, so the side of the square is 20/4=5
find areas:

Area r = 4*6=24.
area S = 5^2 = 25.

ratio is 24:25, or answer b.
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