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# If the perimeter of square region S and the perimeter of

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If the perimeter of square region S and the perimeter of  [#permalink]

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Updated on: 18 Dec 2017, 22:10
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Difficulty:

5% (low)

Question Stats:

90% (02:10) correct 10% (01:37) wrong based on 112 sessions

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If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S

a. 25:16
b. 24:25
c. 5:6
d. 4:5
e. 4:9

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-the-perim ... 27004.html

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Originally posted by aiming4mba on 07 Sep 2010, 12:01.
Last edited by Bunuel on 18 Dec 2017, 22:10, edited 2 times in total.
Edited the question
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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07 Sep 2010, 12:15
2
aiming4mba wrote:
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S
a. 25:16
b. 24:25
c. 5:6
d. 4:5
e. 4:9

Let the side of square be $$s$$ and the side of rectangle $$a$$ and $$b$$

Given: $$\frac{a}{b}=\frac{2}{3}$$ --> $$b=\frac{3a}{2}$$. Also: $$P=4s=2(a+b)$$ --> $$2s=a+b=\frac{5a}{2}$$ --> $$s=\frac{5a}{4}$$.
Question: $$\frac{ab}{s^2}=?$$

$$\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}$$.

Or you can pick numbers: let the sides of rectangle be 4 and 6 (ratio 2:3) then the perimeter of the rectangle will be 2(4+6)=20, thus the side of the square will be 20/4=5. Next, the area of the rectangle will be 4*6=24 and the area of the square will be 5^2=25, so the ratio of the areas will be 24/25.

Or if we take the side of rectangle to be 2x and 3x (for some positive multiple x), then the perimeter of the rectangle will be 2(2x+3x)=10x, thus the side of the square will be 10x/4=5x/2. Next, the area of the rectangle will be 2x*3x=6x^2 and the area of the square will be (5x/2)^2=25x^2/4, so the ratio of the areas will be 24/25.

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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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07 Sep 2010, 12:47
1
aiming4mba wrote:
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S
a. 25:16
b. 24:25
c. 5:6
d. 4:5
e. 4:9

Since sides of R are in 2:3 so why not make the sides 2 and 3? So we have perimeter of rectangle 10
Since square has same perimeter we have 2.5 for each side of square. Now we can double the perimeter of square (for easier calc later) to 20 so each side is 5. To adjust on R we double those sides to so the new sides for R is 4:6 (which reduces to 2:3 so everything's good)

Now we have area of R = 4 * 6 =24 vs area of S = 5 * 5=25 so B
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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06 Feb 2011, 10:16
4s = 2 (l + b)
s = (l + b) / 2
l / b = 2 / 3
l = 2 * b / 3

l * b / s^2 = (2 * b /3) * b / ((l + b)/2)^2 = 8 * b^2/3 / (2 * b / 3 + b)^2 = 24/25 B
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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06 Feb 2011, 10:30
1
Lolaergasheva wrote:
The perimetr of square region S & rectangular region P are equal. If the sides of R are in the ratio 2:3.
The answer is B. I can solve. according the ratio i take rectangular with side 4 and 6. Perimetr=24 perimetr of square with sides length 6 =24. Than areas P=24 S=6^2=36. Where am I wrong?

Rectangle is R; say; l=6, w=4
Perimeter of R= 2(l+w)=2(6+4)=2*10=20 (not 24)
Area of R = 6*4=24

Perimeter of S = Perimeter of R (Given)
Perimeter of S = 4 * side_of_S
Perimeter of R = 20

4*side_of_S = 20
side_of_S, say s = 20/4=5

Area of S = s^2 = 5^2=25

Ratio; Area of R/Area of S = 24/25

Ans: "B"
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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09 Feb 2011, 21:30
Let the sides of the rectangular region R be 2k and 3k

Perimeter of the rectangular region R: 2(2k+3k) = 10k

Perimeter of the square region S: 10k

Thus, length of a side of the square S: 10k/4

Area of Region R: 2k x 3 k = 6(k^2)
Area of Region S: (10k/4)^2= 6.25(k^2)

Ratio: 6/6.25 = 6/(625/100) = 6/(25/4) = 24/25

Ans: 24/25 [Options not given]
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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09 Feb 2011, 22:01
Every time in this same problem I got to the last stage, and always just gave up just before solving the last step.I really don't know why I do that.I always doubt myself when solving a quant problem!!!!!!!!!!
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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09 Feb 2011, 22:03
msneemo wrote:
Every time in this same problem I got to the last stage, and always just gave up just before solving the last step.I really don't know why I do that.I always doubt myself when solving a quant problem!!!!!!!!!!

Don't worry neemo...

How many more days to go by the way? 6?
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Manager
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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09 Feb 2011, 22:09
6 gone already!! Its 5 now...I didnt do anything today..Just cooked lamb chops and watched Friends!!!
Director
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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09 Feb 2011, 22:20
msneemo wrote:
6 gone already!! Its 5 now...I didnt do anything today..Just cooked lamb chops and watched Friends!!!

lol
I squeeze in a "beer day" once a week :D
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Re: If the perimeter of square region S and the perimeter of  [#permalink]

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18 Dec 2017, 22:10
aiming4mba wrote:
If the perimeter of square region S and the perimeter of rectangular region R are equal and the sides of R are in the ratio 2:3 then the ratio of the area of R to the area of S

a. 25:16
b. 24:25
c. 5:6
d. 4:5
e. 4:9

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-the-perim ... 27004.html
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Re: If the perimeter of square region S and the perimeter of   [#permalink] 18 Dec 2017, 22:10
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