Rectangular garden Alpha and circular pond Beta have equal

Hello vjesus12.

Here, you just have to use the area of a rectangular region and a circular region, that is to say: $$A_R=w\cdot l\ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2\ .$$ We know that the dimensions of the rectangular region are 9 and 6. Then $$A_R=9\cdot6\ \ \ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2 $$ $$A_R=54\ \ \ \ \ and\ \ \ \ \ \ \ \ A_C=\pi\ r^2\ .$$ In addition, we know that both regions have the same area, then $$A_R=54\ =\pi\ r^2\ =\ A_C$$ $$\Rightarrow\ \ \ \ r^2=\frac{54}{\pi}$$ $$\Rightarrow\ \ \ \ r=\sqrt{\frac{54}{\pi}}.$$ It implies that the correct asnwer is the option C .

I hope this explanation may help you.

VJesus12 wrote:Rectangular garden Alpha and circular pond Beta have equal area. If garden Alpha is 9 meter by 6 meters, what is the radius of pond Beta?

A) 54Ï€
B) 54/Ï€
C) √(54/π)
D) √(27/π)
E) 27Ï€

The area of Alpha is 9 x 6 = 54. So we use the equation for the area of a circle to determine the radius, r, of Beta:

54 = πr^2

54/Ï€ = r^2

√(54/π) = r

Answer: C