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A circle has the same area with a rectangle. What is the circumference

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MathRevolution
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A circle has the same area with a rectangle. What is the circumference [#permalink] New post   21 Jun 2016, 17:29
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A circle has the same area with a rectangle. What is the circumference of the circle?
1) The perimeter of the rectangle is 18
2) The area of the rectangle is 20

*An answer will be posted in 2 days.
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B
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chetan2u
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Re: A circle has the same area with a rectangle. What is the circumference [#permalink] New post   21 Jun 2016, 20:19
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MathRevolution wrote:
A circle has the same area with a rectangle. What is the circumference of the circle?
1) The perimeter of the rectangle is 18
2) The area of the rectangle is 20

*An answer will be posted in 2 days.


Area of circle = Area of rectangle..

1) The perimeter of the rectangle is 18
Different Area can be possible...
say the sides are 8 and 1.. P = 2(8+1)=18, and A = 8*1 = 8
say the sides are 7 and 2.. 2(7+2)=18, and A = 7*2 = 14
So each of them will give a different circumference of circle
Insuff

2) The area of the rectangle is 20
Area of circle = 20....
so \(\pi*r^2 = 20\)..... we can find \(2*\pi*r\)
suff

B
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Re: A circle has the same area with a rectangle. What is the circumference [#permalink] New post   21 Jun 2016, 23:01
MathRevolution wrote:
A circle has the same area with a rectangle. What is the circumference of the circle?
1) The perimeter of the rectangle is 18
2) The area of the rectangle is 20

*An answer will be posted in 2 days.


Statement 1

Perimeter of rectangle is 18, so a+b is known but I do not know the value of ab.
a+b = 9

a = 6 b =3, ab = 18
a=9, b=1, ab=9.

so different areas will result. Not sufficient.


Taking Statement (2)
Unique value for area is known.
If I have unique area of a circle, then I can get the radius and then I can get circumference. So sufficient.


B is the answer.
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Re: A circle has the same area with a rectangle. What is the circumference [#permalink] New post   26 Jun 2016, 07:28
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We can modify the original condition and the question. The area of the circle and the area of the rectangle are same. Hence, since it is asking for the circumference of the circle, we only have to know the area of the circle (which is same as the area of the rectangle). So, the correct answer is B.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Re: A circle has the same area with a rectangle. What is the circumference [#permalink] New post   12 Jul 2022, 21:30
Given: A circle has the same area with a rectangle.
Asked: What is the circumference of the circle?

1) The perimeter of the rectangle is 18
2(l+b) = 18
l + b = 9
Since there may be many different values for area of the rectangle (lb)
NOT SUFFICIENT

2) The area of the rectangle is 20
\(\pi rˆ2 = 20\)
\(r = \sqrt{20/pi}\)
Circumference = \(2\pi r = 2\pi \sqrt{20/pi} = 4 \sqrt{5pi}\)
SUFFICIENT

IMO B
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Re: A circle has the same area with a rectangle. What is the circumference [#permalink]
12 Jul 2022, 21:30
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