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Math Expert V
Joined: 02 Sep 2009
Posts: 60647
If the circle above has center A and area 144π , what is the perimete  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:40) correct 22% (02:14) wrong based on 54 sessions

### HideShow timer Statistics If the circle above has center A and area 144π, what is the perimeter of sector ABCD?

A. 12+3/2*π

B. 12+3π

C. 18+3/2*π

D. 24+3/2*π

E. 24+3π

Attachment: CircleA.png [ 10.17 KiB | Viewed 1220 times ]

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Senior Manager  G
Joined: 24 Apr 2016
Posts: 313
Re: If the circle above has center A and area 144π , what is the perimete  [#permalink]

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Radius of the circle = 12
Circumference of the circle = 24π

perimeter of sector ABCD = (Radius * 2) + $$\frac{45}{360}$$ * 24π

= 24 + 3π

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
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Joined: 19 Dec 2014
Posts: 15975
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the circle above has center A and area 144π , what is the perimete  [#permalink]

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Hi ALL,

We're told that the circle above has center A and its area is 144pi. We're asked for the perimeter of sector ABCD. This question is based on several Geometry formulas - and we're given all of the necessary numbers to work with - so we just have to work through the appropriate math to answer it.

To start, ABCD is composed of 2 radii and a section of the circumference. That arc is based on a 45-degree angle, so it is 45/360 = 1/8 of the total circumference.

With an area of 144pi, we can solve for the radius:

Area = (pi)(R^2) = 144pi
R^2 = 144
R = 12

With a radius of 12, the total circumference is (2)(pi)(R) = (2)(pi)(12) = 24pi. The arc of ABCD is (1/8)(24pi) = 3pi

Thus, the total perimeter of ABCD is 12+12+3pi = 24 + 3pi

GMAT assassins aren't born, they're made,
Rich
_________________ Re: If the circle above has center A and area 144π , what is the perimete   [#permalink] 02 Dec 2019, 12:04
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# If the circle above has center A and area 144π , what is the perimete  