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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]

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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]

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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]

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New post 03 Feb 2012, 10:17
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]

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

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New post 24 Sep 2013, 01:59
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]

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New post 06 Oct 2014, 09:30
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 :)
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Re: If the perimeter of square region S and the perimeter of rec [#permalink]

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

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

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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


In figure R -

Length = 3 ; Breadth = 2

Area of R = 6 and Perimeter of R = 2 ( 3 + 2 ) => 10

In figure S -

Sides = S (Say)

So, 4s = 10

Or, s = 5/2

Area of S = 25/4

Hence area of R to the area of S = 6 : 25/4 => 24 : 25

Hence, Correct answer will be (B) 24: 25
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Re: If the perimeter of square region S and the perimeter of rec   [#permalink] 02 Nov 2016, 08:57
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