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

[VJesus12]

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

[swerve]

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 \(* 2\)) \(+ \dfrac{45}{360}\ast 24 \pi = 24+3\pi\)