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What is the area of square ABCD ?

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What is the area of square ABCD ? [#permalink]

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13 Sep 2012, 14:06
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What is the area of square ABCD ?

(1) The length of the side of square ABCD is 2.

(2) For square EFGH, which has sides that are 6 longer than those of square ABCD, the ratio of the perimeter to the area is the reciprocal of the corresponding ratio for square ABCD.
[Reveal] Spoiler: OA

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Re: What is the area of square ABCD ? [#permalink]

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13 Sep 2012, 14:40
carcass wrote:
What is the area of square ABCD ?

(1) The length of the side of square ABCD is 2.

(2) For square EFGH, which has sides that are 6 longer than those of square ABCD, the ratio of the perimeter to the area is the reciprocal of the corresponding ratio for square ABCD.

I do not have OA.

1) is clearly suff
2) P/A -----> (6x*4)/6x^2 ---> .............. help

Statement 2
Lets say the side of square ABCD is x & side of square EFGH is x+6
Ratio of Perimeter to area of Square EFGH= Ratio of area to the perimeter of ABCD
--->LHS = RHS
--> $$4(x+6)/(x+6)^2 = (x^2)/4x$$
--> 4/(x+6) = x/4
--> $$x^2 + 6x -16 = 0$$
Solving above equation we get x = either 2 or -8. As side can't be negative, x = 2-----Sufficient.

Hope its clear.
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Last edited by fameatop on 14 Sep 2012, 03:08, edited 1 time in total.

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Re: What is the area of square ABCD ? [#permalink]

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13 Sep 2012, 16:30
fameatop wrote:
carcass wrote:
What is the area of square ABCD ?

(1) The length of the side of square ABCD is 2.

(2) For square EFGH, which has sides that are 6 longer than those of square ABCD, the ratio of the perimeter to the area is the reciprocal of the corresponding ratio for square ABCD.

I do not have OA.

1) is clearly suff
2) P/A -----> (6x*4)/6x^2 ---> .............. help

Statement 2
Lets say the side of square ABCD is x & side of square EFGH is x+6
Ratio of Perimeter to area --> $$4(x+6)/(x+6)^2 = (x^2)/4x$$
--> 4/(x+6) = x/4
--> $$x^2 + 6x -16 = 0$$
Solving above equation we get x = either 2 or -8. As side can't be negative, x = 2-----Sufficient.

Hope its clear.

sorry can you elaborate more clear ?? ok we have P/A ---> 4(x+6)/(x+6)^2 -----> the numerator cancel out and in the denominator we have (x+6)

Then A/P is : x+6/4. How do you have a quadratic equation ??'

Thanks
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Re: What is the area of square ABCD ? [#permalink]

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14 Sep 2012, 04:29
Expert's post
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BOOKMARKED
carcass wrote:
fameatop wrote:
carcass wrote:
What is the area of square ABCD ?

(1) The length of the side of square ABCD is 2.

(2) For square EFGH, which has sides that are 6 longer than those of square ABCD, the ratio of the perimeter to the area is the reciprocal of the corresponding ratio for square ABCD.

I do not have OA.

1) is clearly suff
2) P/A -----> (6x*4)/6x^2 ---> .............. help

Statement 2
Lets say the side of square ABCD is x & side of square EFGH is x+6
Ratio of Perimeter to area --> $$4(x+6)/(x+6)^2 = (x^2)/4x$$
--> 4/(x+6) = x/4
--> $$x^2 + 6x -16 = 0$$
Solving above equation we get x = either 2 or -8. As side can't be negative, x = 2-----Sufficient.

Hope its clear.

sorry can you elaborate more clear ?? ok we have P/A ---> 4(x+6)/(x+6)^2 -----> the numerator cancel out and in the denominator we have (x+6)

Then A/P is : x+6/4. How do you have a quadratic equation ??'

Thanks

The ratio of the perimeter to the area for square square EFGH is $$\frac{4(x+6)}{(x+6)^2}=\frac{4}{x+6}$$;

The ratio of the area to the perimeter for square square ABCD is $$\frac{x^2}{4x}=\frac{x}{4}$$;

We are told that these values are equal, so $$\frac{4}{x+6}=\frac{x}{4}$$. Cross-multiply: $$16=x(x+6)$$ --> $$x^2+6x-16=0$$ --> $$x=2$$ or $$x=-8$$.

Hope it helps.
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Re: What is the area of square ABCD ? [#permalink]

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30 Aug 2014, 03:22
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Re: What is the area of square ABCD ? [#permalink]

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27 Jun 2016, 09:38
Hello from the GMAT Club BumpBot!

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Re: What is the area of square ABCD ?   [#permalink] 27 Jun 2016, 09:38
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