Suppose that the area of a circle is numerically equal to 12 times the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square. Find the length of a side of the square.
A) $\frac { \pi } { 48 }$
B) $\frac { 48 } { \pi }$
C) $48 \pi$

Question

Quizplus · Accepted Answer

Given that the area of the circle is numerically equal to 12 times the perimeter of the square, and the radius of the circle (r) is equal to the side of the square (s), we can set up the equation: $\pi r^2 = 12 \cdot 4s$, because the area of a circle is $\pi r^2$ and the perimeter of a square is $4s$. Simplifying, we get $\pi s^2 = 48s$, and dividing both sides by $\pi s$, we find $s = \frac{48}{\pi}$.

Suppose That the Area of a Circle Is Numerically Equal π48\frac { \pi } { 48 }48π​

Suppose That the Area of a Circle Is Numerically Equal $\frac { \pi } { 48 }$