Chapter 11.5, Problem 8P

To determine

To find the length of the side of the square.

Answer to Problem 8P

  $20.86\text{ cm}$

Explanation of Solution

Given:

The area of the circle that touches the sides of the square is $341.9$ cm².

Calculation:

The area of circle is $341.9$ cm².

  $\begin{array}{l}\pi r^2=341.9\\ r^2=\frac{341.9}{\pi }\\ r^2=\frac{341.9\times 7}{22}\\ r=\sqrt{108.72}\\ r=10.43\text{ cm}\end{array}$

The length of the side of the square will be the diameter of the circle. Hence the length of the side of square is $2\times 10.43\text{ cm}=20.86\text{ cm}$