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A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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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

Originally posted by shyind on 09 Aug 2015, 02:52.
Last edited by Bunuel on 16 Aug 2015, 15:35, edited 1 time in total.
RENAMED THE TOPIC.
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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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shyind wrote:
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

The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: C
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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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shyind wrote:
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

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 [ 17.44 KiB | Viewed 30052 times ]

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A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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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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Math Expert V
Joined: 02 Aug 2009
Posts: 8302
Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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1
Bunuel wrote:
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

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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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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1
Bunuel wrote:
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

Attachment: Untitled.png [ 4.77 KiB | Viewed 7263 times ]

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

So, Circumference will be π*Diameter = 5π

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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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Bunuel wrote:
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

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

Circumference = 2πr = 2π*2.5 = 5π

Correct Option: C
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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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Bunuel wrote:
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

Diagonal will be diameter of the circle.

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

Circumference= π d= 5π

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Re: A 3 by 4 rectangle is inscribed in circle. What is the circumference  [#permalink]

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Bunuel wrote:
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

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

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