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

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Carcass
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The area of a circular sign whose radius is 6 feet, is 3 times the are [#permalink] New post   11 Jun 2021, 06:25
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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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C
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Re: The area of a circular sign whose radius is 6 feet, is 3 times the are [#permalink] New post   11 Jun 2021, 06:28
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Carcass 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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Re: The area of a circular sign whose radius is 6 feet, is 3 times the are [#permalink] New post   29 Nov 2022, 22:33
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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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