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Geometry Problem

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by Gurpinder » Sun Aug 15, 2010 7:34 pm
Hmm....can you please post the official answer. I just want to make sure before posting.
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by RickH » Sun Aug 15, 2010 8:15 pm
If i remeber correctly the correct answer should be 24:25.
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by vijaynaik » Sun Aug 15, 2010 8:56 pm
Lets say R has sides l , w then perimeter is 2(l+w).
l and w are in 2:3 ratio.
p(R) = 2(2x+3x);

Square S side is a. P(S) = 4a.
since P(S) = p(R)
4a = 10x ;

area of R, A(R) = 2x * 3x = 6x^2;
A(s) = a^2 = (5/2*x)^2;

A(R)/A(S) = 6x^2/ (25x^2 /4) = 24/25;

Ratio is 24:25;
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by RickH » Mon Aug 16, 2010 4:57 am
Great, thanks!
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by GMATGuruNY » Mon Aug 16, 2010 6:51 am
RickH wrote:Please help me with this problem:

The perimeter of square region S and rectangular 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 Region S?

Thanks!
When a problem asks for a ratio, we can plug in our own values. In this problem, we need to plug in values for the dimensions of the rectangle and for those of the square.

Rectangle:
w = 4
l = 6
p = 4+4+6+6 = 20
a = 4*6 = 24

Square:
p = 20 (same as rectangle)
s = 20/4 = 5
a = 5*5 = 25

R/S = 24/25.
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by RickH » Mon Aug 16, 2010 6:54 am
GMATGuruNY wrote:
RickH wrote:Please help me with this problem:

The perimeter of square region S and rectangular 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 Region S?

Thanks!
When a problem asks for a ratio, we can plug in our own values. In this problem, we need to plug in values for the dimensions of the rectangle and for those of the square.

Rectangle:
w = 4
l = 6
p = 4+4+6+6 = 20
a = 4*6 = 24

Square:
p = 20 (same as rectangle)
s = 20/4 = 5
a = 5*5 = 25

R/S = 24/25.
That is even simpler, I actually tried that variation but with side length 2 and 3. Thanks!
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by beatthegmatinsept » Mon Aug 16, 2010 2:45 pm
Good Question. I didn't plug in numbers, used variables instead. Got 24:25. Whats the source here?
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