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

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

A. \(12+\dfrac3{2\pi}\)

B. \(12+3\pi\)

C. \(18+\dfrac3{2\pi}\)

D. \(24+\dfrac3{2\pi}\)

E. \(24+3\pi\)

Answer: E

Source: Veritas Prep

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VJesus12 wrote:
Wed Aug 18, 2021 7:34 am
CircleA.png

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

A. \(12+\dfrac3{2\pi}\)

B. \(12+3\pi\)

C. \(18+\dfrac3{2\pi}\)

D. \(24+\dfrac3{2\pi}\)

E. \(24+3\pi\)

Answer: E

Source: Veritas Prep
Radius of the circle \(= 12\)
Circumference of the circle \(= 24\pi\)

perimeter of sector \(ABCD =\) (Radius \(* 2\)) \(+ \dfrac{45}{360}\ast 24 \pi = 24+3\pi\)