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# If a square of side x and a circle of radius r have equal areas, what

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Math Expert
Joined: 02 Sep 2009
Posts: 56304
If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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10 Jan 2019, 02:57
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If a square of side x and a circle of radius r have equal areas, what is the ratio x/r ?

A. $$\frac{2}{\pi}$$

B. $$\sqrt{\pi}$$

C. $$\frac{\pi}{2}$$

D. $$\pi$$

E. $$\pi^2$$

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Joined: 01 May 2017
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Location: India
Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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10 Jan 2019, 03:51
If a square of side x and a circle of radius r have equal areas, what is the ratio x/r ?

Area of the square of side $$x = x^2$$
Area of the Circle of radius $$r = Pi*r^2$$
Both are equal implies
$$x^2 = Pi*r^2$$
$$x/r = \sqrt{Pi}$$

Option B is correct
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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10 Jan 2019, 06:43

Solution

Given:
• Side of a square = x
• Radius of a circle = r
• Both square and circle have equal areas

To find:
• The ratio of $$\frac{x}{r}$$

Approach and Working:
• Area of square = $$x^2$$
• Area of circle = $$ᴨr^2$$
• We are given that, $$ᴨr^2 = x^2$$

Thus, $$\frac{x}{r} = √ᴨ$$

Hence, the correct answer is Option B

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Concentration: Sustainability, Marketing
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Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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10 Jan 2019, 07:16
Bunuel wrote:
If a square of side x and a circle of radius r have equal areas, what is the ratio x/r ?

A. $$\frac{2}{\pi}$$

B. $$\sqrt{\pi}$$

C. $$\frac{\pi}{2}$$

D. $$\pi$$

E. $$\pi^2$$

x^2= pi * r^2
x/r = sqrt pi
IMO B
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Re: If a square of side x and a circle of radius r have equal areas, what   [#permalink] 10 Jan 2019, 07:16
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