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Re: If the circle above has center A and area 144π , what is the perimete [#permalink]
Expert Reply
Solution:

The area if the circle \(= 144\pi\)

We know area of circle \(= \pi\times radius^2\)

Sow e cab write: \(= \pi\times radius^2=144\pi\)

\(⇒ radius^2=144\)

\(⇒ radius = 12\)

So no we know the radius of this circle \(= 12\)

We already know the radius. Now we just want the length of arc BCD to get our asnwer.

Arc BCD \(= \frac{45}{360} \times 2\pi \times radius = \frac{1}{8} \times 2\pi \times 12 = 3\pi\).

Perimeter of sector \(ABCD = radius AB+arc BCD+radius DA = 12+3\pi+12=24+3\pi\)

Hence the right answer is Option E.
GMAT Club Bot
Re: If the circle above has center A and area 144π , what is the perimete [#permalink]
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