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505-555 (Easy)|   Geometry|      
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shyind
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A 3 by 4 rectangle is inscribed in circle. What is the circumference Updated on: 16 Aug 2015, 16:35
Originally posted by shyind on 09 Aug 2015, 03:52.
Last edited by Bunuel on 16 Aug 2015, 16:35, edited 1 time in total.
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C
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15% (low)

Question Stats:

80% (00:48) correct 20% (00:52) wrong based on 81 sessions

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A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
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C
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 09 Aug 2015, 05:10
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shyind
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more

The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: C
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 09 Aug 2015, 05:12
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shyind
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more

The rectangle will be positioned such that the diagonal of the rectangle will become the diameter of the circle. This is true as the triangle in a semi circle with diameter as the base makes a 90 degree at the circumference.

Thus, the diameter of the circle = \(\sqrt{3^2+4^2}\) = 5 ---> Circumference = \(\pi\) d = 5\(\pi\). C is the correct answer.
Attachments

rect in a circle.JPG
rect in a circle.JPG [ 17.44 KiB | Viewed 48021 times ]

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A 3 by 4 rectangle is inscribed in circle. What is the circumference 22 May 2016, 13:47
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A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 22 May 2016, 20:31
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Bunuel
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more


POINT to remember -
If you are inscribing a rectangle in a circle, the Diagonal of rectangle will always pass through center of circle and thus Diagonal will be equal to Radius..

lets solve -
diagonal of rectangle = \(\sqrt{3}^2+\sqrt{4}^2\) = 5..
thus Dia of circle = 5..
Circumference = dia*pi = 5π
C
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 23 May 2016, 11:48
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Bunuel
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more

Attachment:
Untitled.png
Untitled.png [ 4.77 KiB | Viewed 23359 times ]

Using pythagoras theorem we can find the diameter of the circle as 5

So, Circumference will be π*Diameter = 5π

Answer will be (C)
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 24 May 2016, 04:11
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Bunuel
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more
If a rectangle is inscribed in a circle, then the diagonal of the rectangle = diameter of the circle.
In this case, diagonal = (9 + 16)^(1/2) = 5

Hence the radius = 2.5

Circumference = 2πr = 2π*2.5 = 5π

Correct Option: C
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 24 May 2016, 05:21
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Bunuel
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more

Diagonal will be diameter of the circle.

(3^2 + 4^2)^1/2= 5

Circumference= π d= 5π

C is the answer
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 24 May 2016, 06:52
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Bunuel
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?

A. 2.5π
B. 3π
C. 5π
D. 4π
E. 10π
Show more

With Sides 3 and 4, the rectangle have diagonal equal to 5 (3-4-5 triangle)

P.S. Since any angle drawn at circumference in semicircle is 90 degrees therefore the diagonals will be the diameter of the circle

Circumference of Circle = π *Diameter = 5π

Answer: Option C
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A 3 by 4 rectangle is inscribed in circle. What is the circumference 27 Sep 2020, 01:18
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