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

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If the perimeter of square region S and the perimeter of rec [#permalink] New post 03 Feb 2012, 07:21
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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
[Reveal] Spoiler: OA

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Re: the primeters of square and rectangle [#permalink] New post 03 Feb 2012, 07:29
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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

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}.

Answer: B.

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.

Answer: B.

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.

Answer: B.
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Re: If the perimeter of square region S and the perimeter of rec [#permalink] New post 03 Feb 2012, 09:17
GOT IT, 2ND APPROACH IS EASIER...THAAAAAANKS B.
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Re: If the perimeter of square region S and the perimeter of rec [#permalink] New post 20 Jun 2013, 05:39
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Re: If the perimeter of square region S and the perimeter of rec [#permalink] New post 24 Sep 2013, 00:59
manalq8 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


help needed please


We know Perimeter of a square (Ps) = 4*side
Perimeter of a rectangle (Pr) = 2(length+breath)

Let us assume 40 to be the perimeter of the square (since we know each side of a square is equal and the perimeter is divisible by 4, also take in to account the length and breadth of the rectangle is in the ration 2k:3k = 5k; we can assume such a number)

Therefore,
Ps = Pr = 40
Area of the square = 100 sq. units
We know 2(length+breadth) = 40
i.e. length + breadth = 20 (or 5k = 20 given that l:b (or b:l) = 2:3)
Therefore length = 8, breath = 12

Area of the rectangle = 8*12 = 96 sq. units

Question asked = Area of the rectangle : Area of the square = 96:100 ==> 24:25

Note : The explanation might be bigger, but it takes less than 15 seconds to solve this problem if you assume numbers and try the problem.
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Re: If the perimeter of square region S and the perimeter of rec [#permalink] New post 06 Oct 2014, 08:30
Bunuel has given a pretty good explanation. But still,, here is how i approached it :
For rectangle of length a and Breadth b: given is a/b = 2/3 ie a =2x/5 and b=3x/5(where x is some multiplication factor of the ratio). So, Perimeter of R = 2(a+b) = 2(2x/5 + 3x/5) = 2x
Perimeter of S = 4Side = 2x Therefore Side = x/2.
Area R (a*b):Area S side^2 = 6x^2/25 / x^2/4 = 24:25 .

:) Hope i could help :)
Re: If the perimeter of square region S and the perimeter of rec   [#permalink] 06 Oct 2014, 08:30
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