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# If the circle above has center A and area 144π , what is the perimete

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