Suppose that the area of a circle is numerically equal to 2 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) $\frac { \pi } { 8 }$
B) $8 \pi$
C) $\frac { \pi } { 16 }$
D) $\frac { 8 } { \pi }$
E) $\frac { 16 } { \pi }$

Question

Quizplus · Accepted Answer

Let the length of a side of the square (and the radius of the circle) be $r$. The area of the circle is $\pi r^2$, and the perimeter of the square is $4r$. According to the problem, $\pi r^2 = 2 \times 4r$, which simplifies to $\pi r^2 = 8r$. Dividing both sides by $\pi r$, we get $r = \frac{8}{\pi}$.

Suppose That the Area of a Circle Is Numerically Equal π8\frac { \pi } { 8 }8π​

Suppose That the Area of a Circle Is Numerically Equal $\frac { \pi } { 8 }$