A circle and a square have the same area. What is the ratio

Question

A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A)  2 : \sqrt{(2\pi)} 
(B)  1 : 2\sqrt{\pi} 
(C)  2\sqrt{\pi} : \sqrt{2} 
(D)  1 : \sqrt{2} 
(E)  1 : 2\pi

zisis · Answer

IMO A

diameter 20,
radius= 10
πr^2 = 100π
area = 100π
side =  \sqrt{100\pi} 
diagonal =  Side * \sqrt{2} = 10\sqrt{(2\pi)}

ratio
 20 : 10\sqrt{(2\pi)} 
=  2 : \sqrt{(2\pi)}

Bunuel · Answer

area_{circle}=\pi{\frac{diameter^2}{4}}=area_{square}=\frac{diagonal^2}{2} ;

\pi{\frac{diameter^2}{4}}=\frac{diagonal^2}{2} ;

\frac{diameter^2}{diagonal^2}=\frac{2}{\pi} ;

\frac{diameter}{diagonal}=\frac{\sqrt{2}}{\sqrt{\pi}}=\frac{2}{\sqrt{2\pi}} .

Answer: A.

Pleas format the answers properly.

shrouded1 · Answer

\pi r^2 = a^2

\frac{r}{a} = \frac{1}{\sqrt{\pi}}

\frac{2r}{\sqrt{2}a} = \frac{2}{\sqrt{2\pi}}

Hence A

zisis · Answer

Had to copy and paste (pi). Is there a better way?

Posted from my mobile device

Bunuel · Answer

Mark \pi by button. Also check: https://gmatclub.com/forum/writing-mathe ... 72468.html hope it helps.

Vips0000 · Answer

Diameter be D and diagonal be y then D/Y = ?
given is area of square = area of circle
=> 1/2*Y^2 = 1/4*pi*D^2
=>D/Y= sqrt(2/pi) = 2/sqrt(2pi)

Ans A it is.

PareshGmat · Answer

Refer diagram below:

\pi r^2 = a^2

a = \sqrt{\pi}r

\frac{Diameter of circle}{Diagonal of Square} = \frac{2r}{\sqrt{2} \sqrt{\pi}r}

Answer = \frac{2}{\sqrt{2 \pi}  = A

PareshGmat · Answer

Answer = A

Let the area of circle = area of square = 1

\pi r^2 = 1

r = \frac{1}{\sqrt{\pi}}

2r = diameter  = \frac{2}{\sqrt{\pi}}

Side of square = 1

Diagonal  = \sqrt{2}

Ratio  = \frac{2}{\sqrt{2*\pi}}

JeffTargetTestPrep · Answer

Let us denote the length of a side of the square by s and the radius of the circle by r.

We can create the equation:

πr^2 = s^2

r√π = s

Since the side of the square s = r√π, the diagonal of the square is r√π x √2 = r√(2π).

The diameter of the circle is 2r. Thus, the ratio of the diameter of the circle to the diagonal of the square is:

2r/  = 2/√(2π)

Answer: A

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A circle and a square have the same area. What is the ratio

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A circle and a square have the same area. What is the ratio

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