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# A circular region and a square region have the same area. What is the

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Math Expert
Joined: 02 Sep 2009
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A circular region and a square region have the same area. What is the [#permalink]

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16 Nov 2017, 22:58
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A circular region and a square region have the same area. What is the ratio of the side of the square to the diameter of the circle?

(A) √π/π
(B) √π/2
(C) 2/π
(D) π/4
(E) π/2

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Re: A circular region and a square region have the same area. What is the [#permalink]

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17 Nov 2017, 00:40
Area of the circle via diamter = P*d^2/4
Area of square = a^2
P*d^2/4=a^2
P^1/2 / 2 = a/d
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Re: A circular region and a square region have the same area. What is the [#permalink]

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17 Nov 2017, 08:56
Bunuel wrote:
A circular region and a square region have the same area. What is the ratio of the side of the square to the diameter of the circle?

(A) √π/π
(B) √π/2
(C) 2/π
(D) π/4
(E) π/2

$$a^2 = πr^2$$

$$a = \sqrt{π}r$$

So, $$a : r$$ = $$\sqrt{π}$$

Now, $$a : 2r = \frac{√π}{2}$$

Or, $$a : d = \frac{√π}{2}$$, answer will be (B)
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A circular region and a square region have the same area. What is the [#permalink]

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17 Nov 2017, 11:08
Bunuel wrote:
A circular region and a square region have the same area. What is the ratio of the side of the square to the diameter of the circle?

(A) √π/π
(B) √π/2
(C) 2/π
(D) π/4
(E) π/2

Area of square = area of circle

$$s^2 = πr^2$$
$$\sqrt{s^2}=\sqrt{π}*\sqrt{r^2}$$
$$s = \sqrt{π}*r$$
$$r = \frac{1}{2}d$$, so

$$s=\sqrt{π}*r=\sqrt{π}*\frac{1}{2}d=$$ $$\frac{\sqrt{π}d}{2}$$

Ratio of side of square, s, to diameter, d?

$$\frac{\frac{√π(d)}{2}}{d}=\frac{√π(d)}{2d}=\frac{√π}{2}$$

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Re: A circular region and a square region have the same area. What is the [#permalink]

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17 Nov 2017, 14:13
Bunuel wrote:
A circular region and a square region have the same area. What is the ratio of the side of the square to the diameter of the circle?

(A) √π/π
(B) √π/2
(C) 2/π
(D) π/4
(E) π/2

s^2=πr^2
s=r√π
s/2r=r√π/2r=√π/2
B
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Re: A circular region and a square region have the same area. What is the [#permalink]

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20 Nov 2017, 12:24
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Bunuel wrote:
A circular region and a square region have the same area. What is the ratio of the side of the square to the diameter of the circle?

(A) √π/π
(B) √π/2
(C) 2/π
(D) π/4
(E) π/2

We can create the equation:

s^2 = πr^2

s = r√π

s/r = √π

s/(2r) = √π/2

s/d = √π/2

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Re: A circular region and a square region have the same area. What is the   [#permalink] 20 Nov 2017, 12:24
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