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Rectangle DKNY with length 12 and width 5 is inscribed within the abo

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Rectangle DKNY with length 12 and width 5 is inscribed within the abo  [#permalink]

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New post 31 May 2015, 03:14
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A
B
C
D
E

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89% (00:50) correct 11% (01:26) wrong based on 43 sessions

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Rectangle DKNY with length 12 and width 5 is inscribed within the above circle. What is the circumference of the circle?

A. 6.5π
B. 13π
C. 60
D. 42.25π
E. 169π
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Re: Rectangle DKNY with length 12 and width 5 is inscribed within the abo  [#permalink]

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New post 31 May 2015, 18:30
1
reto wrote:
Attachment:
E7793ad.png
Rectangle DKNY with length 12 and width 5 is inscribed within the above circle. What is the circumference of the circle?

A. 6.5π
B. 13π
C. 60
D. 42.25π
E. 169π


The diagonal of the rectangle is 13 from Pythagoras theorem. The diagonal will be same as the diameter of the circle. hence circumference = pie*d. option B

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Re: Rectangle DKNY with length 12 and width 5 is inscribed within the abo  [#permalink]

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New post 31 May 2015, 20:35
1
reto wrote:
Attachment:
E7793ad.png
Rectangle DKNY with length 12 and width 5 is inscribed within the above circle. What is the circumference of the circle?

A. 6.5π
B. 13π
C. 60
D. 42.25π
E. 169π


Explanation why the diagonal of the rectangle will be the same as the diameter of the circle: we have a corner of the rectangle at 90 degree. Now the diagonal of the rectangle and the 90 degree creates/matches angle of semi circle concept.... The diameter makes 90 degree on the circumference.... Thus, the diagonal of the rectangle and the diameter of the subscribed circle must be the same!

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Re: Rectangle DKNY with length 12 and width 5 is inscribed within the abo  [#permalink]

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New post 31 May 2015, 22:53
Diagonal of rectangle = diameter of circle = d = sqrt(12^2++5^2)
d=13

Circumference = 2πr = πd= 13π

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Re: Rectangle DKNY with length 12 and width 5 is inscribed within the abo  [#permalink]

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New post 31 May 2015, 23:08
1
1
reto wrote:
Attachment:
E7793ad.png
Rectangle DKNY with length 12 and width 5 is inscribed within the above circle. What is the circumference of the circle?

A. 6.5π
B. 13π
C. 60
D. 42.25π
E. 169π


Check out the following posts. They discuss inscribing polygons into circles and circles into polygons.

http://www.veritasprep.com/blog/2013/06 ... d-circles/
http://www.veritasprep.com/blog/2013/07 ... relations/
http://www.veritasprep.com/blog/2013/07 ... n-circles/
http://www.veritasprep.com/blog/2013/07 ... -polygons/
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Re: Rectangle DKNY with length 12 and width 5 is inscribed within the abo   [#permalink] 31 May 2015, 23:08
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