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If the perimeter of square region S and the perimeter of rec
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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
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If the perimeter of square region S and the perimeter of rec
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03 Feb 2012, 07:29
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: The sides of R are in the ratio 2:3 > \(\frac{a}{b}=\frac{2}{3}\) > \(b=\frac{3a}{2}\). The perimeter of square region S and the perimeter of rectangular region R are equal > \(P=4s=2(a+b)\) > \(2s=a+b=\frac{5a}{2}\) > \(s=\frac{5a}{4}\). Question: \(\frac{area \ of \ R}{area \ of \ S}=\frac{ab}{s^2}=?\) Substitute b = 3a/2 and s = 5a/4 into the question: \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). 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. Similar question: https://gmatclub.com/forum/iftheperim ... 96132.html
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Re: If the perimeter of square region S and the perimeter of rec
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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
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Re: If the perimeter of square region S and the perimeter of rec
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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
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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



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Re: If the perimeter of square region S and the perimeter of rec
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02 Nov 2016, 07:57
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
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12 Jun 2018, 07:00
Bunuel 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: \(\frac{ab}{s^2}=?\) \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). 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. Similar question: https://gmatclub.com/forum/iftheperim ... 96132.html hi pushpitkc, can you explain how after this \(s=\frac{5a}{4}\). we got this > \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). thanks



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If the perimeter of square region S and the perimeter of rec
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12 Jun 2018, 08:48
dave13 wrote: Bunuel 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: \(\frac{ab}{s^2}=?\) \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). 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. Similar question: https://gmatclub.com/forum/iftheperim ... 96132.html hi pushpitkc, can you explain how after this \(s=\frac{5a}{4}\). we got this > \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). thanks Hi dave13Rectangle: Length  a , Breadth  b  Square: size  s. We know that \(b=\frac{3a}{2}\) and \(s=\frac{5a}{4}\) Ratio of area = \(\frac{ab}{s^2}\) = \(\frac{\frac{3a^2}{2}}{\frac{25a^2}{16}}\) = \({\frac{3a^2}{2}}*{\frac{16}{25a^2}} = \frac{24}{25}\) Hope this clears your confusion!
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Re: If the perimeter of square region S and the perimeter of rec
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12 Jun 2018, 13:08
pushpitkc wrote: dave13 wrote: Bunuel 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: \(\frac{ab}{s^2}=?\) \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). 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. Similar question: https://gmatclub.com/forum/iftheperim ... 96132.html hi pushpitkc, can you explain how after this \(s=\frac{5a}{4}\). we got this > \(\frac{ab}{s^2}=\frac{3a^2}{2}*\frac{16}{25a^2}=\frac{24}{25}\). thanks Hi dave13Rectangle: Length  a , Breadth  b  Square: size  s. We know that \(b=\frac{3a}{2}\) and \(s=\frac{5a}{4}\) Ratio of area = \(\frac{ab}{s^2}\) = \(\frac{\frac{3a^2}{2}}{\frac{25a^2}{16}}\) = \({\frac{3a^2}{2}}*{\frac{16}{25a^2}} = \frac{24}{25}\) Hope this clears your confusion! Hi pushpitkc, appreciate your explanation just one question just one question we need to find ratio of area of rectangle to the area of square but we know only breadth of rectangle \(b=\frac{3a}{2}\) i mean it doesnt represent the area of rectangle whereas area of square is aexprresed correctly \(s=\frac{5a}{4}\) my question is: why do we divide only breadth of rectangle by area of square AND NOT area of rectangle by area of square



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Re: If the perimeter of square region S and the perimeter of rec
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12 Jun 2018, 22:01
dave13 wrote: pushpitkc wrote: dave13 wrote: Hi dave13Rectangle: Length  a , Breadth  b  Square: size  s. We know that \(b=\frac{3a}{2}\) and \(s=\frac{5a}{4}\) Ratio of area = \(\frac{ab}{s^2}\) = \(\frac{\frac{3a^2}{2}}{\frac{25a^2}{16}}\) = \({\frac{3a^2}{2}}*{\frac{16}{25a^2}} = \frac{24}{25}\) Hope this clears your confusion! Hi pushpitkc, appreciate your explanation just one question just one question we need to find ratio of area of rectangle to the area of square but we know only breadth of rectangle \(b=\frac{3a}{2}\) i mean it doesnt represent the area of rectangle whereas area of square is aexprresed correctly \(s=\frac{5a}{4}\) my question is: why do we divide only breadth of rectangle by area of square AND NOT area of rectangle by area of square Hi dave13The area of the rectangle is length*breadth = a*b. We know that the breadth \(b=\frac{3a}{2}\). The area of the rectangle will be \(a*b = a*\frac{3a}{2} = \frac{3a^2}{2}\) Hope this helps you!
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Re: If the perimeter of square region S and the perimeter of rec
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14 Jun 2018, 09:33
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 We are given that the perimeters of square region S and rectangular region R are equal and that the sides of R are in the ratio 2 : 3. Let’s label the sides of our figures: Width of rectangle R = 2x Length of rectangle R = 3x Side of square S = s The perimeter of rectangular region R is 2(2x) + 2(3x) = 4x + 6x = 10x. The perimeter of square region S is 4s. Since the two perimeters are equal we can create the following equation: 4s = 10x 2s = 5x s = (5/2)x Lastly, we need to determine the areas of both rectangle R and square S. Area of rectangle R = length * width A = (3x)(2x) = 6x^2 Since s = (5/2)x, we can use (5/2)x for the side of S. Area of square S = side^2 A = [(5/2)x]^2 A = (25x^2)/4 We must determine the ratio of the area of region R to the area of region S. Area of R/Area of S 6x^2/[(25x^2)/4] 6/(25/4) 24/25 Alternate Solution: We know the sides of the rectangle have a ratio of 2:3; thus we can express the sides of this rectangle as 2x and 3x for some number x. The perimeter of the rectangle, in terms of x, is then 3x + 2x + 3x + 2x = 10x. This is also the perimeter of the square, so taking x = 2 will give us easy numbers to work with. When x = 2, the sides of the rectangle are 4 and 6; thus the area of the rectangle is 4 x 6 = 24. Also, when x = 2, the perimeter of the square is 10x = 20; thus a side of the square will be 5. The area of the square will then be 5 x 5 = 25. So, the ratio of the area of the rectangle to the area of the square is 24:25. Answer: B
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Re: If the perimeter of square region S and the perimeter of rec
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14 Jun 2018, 12:06
yes it's B
We just need to know the formulae of the perimeter of the square and the perimeter of the rectangle.




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