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

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed Aug 18, 2021 7:34 am

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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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Source: Beat The GMAT — Problem Solving | Wed Aug 18, 2021 7:34 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Wed Aug 18, 2021 1:24 pm

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

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