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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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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


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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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

Attachment:
Untitled.png
Untitled.png [ 4.77 KiB | Viewed 23346 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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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
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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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

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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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

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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