The area of a circular sign whose radius is 6 feet, is 3...

Hi Luandato,


Okay, so let's start with what we know.

Radius, r = 6 ft.

Therefore, we can get the area of the circle:

$$A= \pi\times r^2$$
$$A =\pi\times 6^2$$
$$A = 36\pi$$

Now, we know that the area of the circle is 3 times the area of the rectangle, so

$$A (Rectangle) = \frac{36\pi}{3} = 12\pi$$

The equation for the area of ANY rectangle is as follows:

$$A (rectangle) = length\ \times\ width$$

And we know that the length is twice the width:

$$length\ =\ 2\times width$$

So we know that the area is:


$$A (rectangle) = \left(2\times width\right)\ \times\ \left(width\right)\ =\ 2\times width^2$$

Combining this equation with the above equation leads to:
$$12\pi = \ 2\times width^2$$

So the width is:
$$width\ =\ \sqrt{\frac{12\times \pi }{2}} =\sqrt{6\pi}$$

And since we know that the length is twice the width, we have


$$length\ =\ 2\ \times width\ =\ 2\sqrt{6\pi}$$

Answer choice C.

Best,
-OWN