If the circle above has center \(A\) and area \(144\pi\),

[M7MBA]

If the circle above has center \(A\) and area \(144\pi\), what is the perimeter of sector \(ABCD?\)

A. \(12+\dfrac32\pi\)

B. \(12+3\pi\)

C. \(18+\dfrac32\pi\)

D. \(24+\dfrac32\pi\)

E. \(24+3\pi\)

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

[[email protected]]

Hi M7MBA,

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

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Scott@TargetTestPrep]

If the circle above has center \(A\) and area \(144\pi\), what is the perimeter of sector \(ABCD?\)

A. \(12+\dfrac32\pi\)

B. \(12+3\pi\)

C. \(18+\dfrac32\pi\)

D. \(24+\dfrac32\pi\)

E. \(24+3\pi\)

[spoiler]OA=E[/spoiler]

Source: Veritas Prep

Since the area is 144π, the radius is 12, so the sum of radii AB and AD is 24.

Since the diameter is 24, the circumference is 24π. Thus, arc BCD has a length of 45/360 x 24π = 1/8 x 24π = 3π. Therefore, the perimeter of sector ABCD is 24 + 3π.

Answer: E