Answer:
The length of the sides of the square is approximately 11.239 centimeters.
Step-by-step explanation:
Since the circle is inscribed in the square, the length of each side of the square ([tex]l[/tex]), in centimeters, is equal to the length of the diameter of the circle ([tex]D[/tex]), in centimeters. The area of the circle ([tex]A_{c}[/tex]), in square centimeters:
[tex]A_{c} = \frac{\pi\cdot D^{2}}{4}[/tex] (1)
Where [tex]D[/tex] is the diameter of the circle, in centimeters.
If we know that [tex]A_{c} = 99.2\,cm^{2}[/tex], then the length of the sides of the square is:
[tex]D = \sqrt{\frac{4\cdot A_{c}}{\pi} }[/tex]
[tex]l = D \approx 11.239\,cm[/tex]
The length of the sides of the square is approximately 11.239 centimeters.
