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What is the perimeter of sector ABCD?

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What is the perimeter of sector ABCD?

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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

The OA is E.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

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GMAT/MBA Expert

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Hello LUANDATO.

Let's take a look at your question.

First, if the area of the circle is 144π, then r=12.

Also, If we use that the length of an arc of a circumference is $$L=r\cdot\theta$$ then we got $$L(BD)=12\cdot45º=12\cdot\frac{\pi}{4}=3\pi.$$ So, the perimeter of ABCD is $$AB+BC+CD+DA=AB+BD+AB=12+3\pi+12=24+3\pi.$$ So, the correct option is E .

I hope this explanation can help you.

I'm available if you'd like a follow up.

Regards,

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