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!
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Gurpinder
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Hmm....can you please post the official answer. I just want to make sure before posting.
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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;
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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GMATGuruNY
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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.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!
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
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That is even simpler, I actually tried that variation but with side length 2 and 3. Thanks!GMATGuruNY wrote: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.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!
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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beatthegmatinsept
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Good Question. I didn't plug in numbers, used variables instead. Got 24:25. Whats the source here?
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