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

Question

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

D3N0 · Answer

The diagonal of the rectangle will be the diameter of the circle.
and perimeter= 2*pi*r
Ans: C

ENGRTOMBA2018 · Answer

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.

Bunuel · Answer

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

chetan2u · Answer

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

Abhishek009 · Answer

Untitled.png Using pythagoras theorem we can find the diameter of the circle as 5 So, Circumference will be π*Diameter = 5π Answer will be (C)

OptimusPrepJanielle · Answer

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

Divyadisha · Answer

Diagonal will be diameter of the circle.

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

Circumference= π d= 5π

C is the answer

GMATinsight · Answer

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

bumpbot · Answer

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

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

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