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What is the area of square ABCD ?

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carcass
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What is the area of square ABCD ? [#permalink] New post   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.
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fameatop
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Re: What is the area of square ABCD ? [#permalink] New post   Updated on: 14 Sep 2012, 03:08
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

:)


Answer is D
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.

Answer D

Hope its clear.

Originally posted by fameatop on 13 Sep 2012, 14:40.
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] New post   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

:)


Answer is D
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.

Answer D

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] New post   14 Sep 2012, 04:29
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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

:)


Answer is D
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.

Answer D

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] New post   19 Apr 2023, 04:53
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Re: What is the area of square ABCD ? [#permalink]
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