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The area of a circular sign whose radius is 6 feet, is 3 times the are
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11 Jun 2021, 06:25
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\(\sqrt{\pi}\)
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
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11 Jun 2021, 06:28
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\(\sqrt{\pi}\)
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
Re: The area of a circular sign whose radius is 6 feet, is 3 times the are
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29 Nov 2022, 22:33
29 Nov 2022, 22:33
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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