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The area of a circular sign whose radius is 6 feet, is 3 times the are

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The area of a circular sign whose radius is 6 feet, is 3 times the are  [#permalink]

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New post 22 Apr 2017, 19:29
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The area of a circular sign whose radius is 6 feet, is 3 times the area of a rectangular sign whose length is twice its width. What is the length, in feet, of the rectangular sign?

A) \(\sqrt{6\pi}\)

B) 3\(\sqrt{\pi}\)

C) 2\(\sqrt{6\pi}\)

D) 6\(\sqrt{\pi}\)

E) 12\(\sqrt{\pi}\)
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Re: The area of a circular sign whose radius is 6 feet, is 3 times the are  [#permalink]

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New post 22 Apr 2017, 20:12
LakerFan24 wrote:
The area of a circular sign whose radius is 6 feet, is 3 times the area of a rectangular sign whose length is twice its width. What is the length, in feet, of the rectangular sign?

A) \(\sqrt{6\pi}\)

B) 3\(\sqrt{\pi}\)

C) 2\(\sqrt{6\pi}\)

D) 6\(\sqrt{\pi}\)

E) 12\(\sqrt{\pi}\)



length =l width =w
l/2=w
area rect. = l*l/2
area of circle = 36π

as per stem
36π= l^2/2
thus l = 2 √ 6π

Ans C
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Re: The area of a circular sign whose radius is 6 feet, is 3 times the are  [#permalink]

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New post 26 Nov 2017, 12:21
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LakerFan24 wrote:
The area of a circular sign whose radius is 6 feet, is 3 times the area of a rectangular sign whose length is twice its width. What is the length, in feet, of the rectangular sign?

A) \(\sqrt{6\pi}\)

B) 3\(\sqrt{\pi}\)

C) 2\(\sqrt{6\pi}\)

D) 6\(\sqrt{\pi}\)

E) 12\(\sqrt{\pi}\)


Area of a circular sign whose radius is 6 feet
Area = π(radius)²
= π(6)²
= 36π

Area of a rectangular sign whose length is twice its width.
Let x = width
So, 2x = length
Area of rectangle = (length)(width)
= (2x)(x)
= 2x²

Area of a circular sign is 3 times the area of a rectangular sign.
Area of a circular sign = 3(area of a rectangular sign)
36π = 3(2x²)
Simplify right side: 36π = 6x²
Divide both sides by 6 to get: 6π = x²
So, x = √(6π)
In other words, the width = √(6π) feet
Since the length is TWICE the width, the length = 2√(6π) feet
Answer: C

Cheers,
Brent
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Brent Hanneson – GMATPrepNow.com
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Re: The area of a circular sign whose radius is 6 feet, is 3 times the are &nbs [#permalink] 26 Nov 2017, 12:21
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