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)

=

2x²Area 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

_________________

Brent Hanneson – Founder of gmatprepnow.com