Answer
The length of the radius of the circle is 7 cm.
Work Step by Step
Let X represent the length of the radius of the circle.
The length of the side of the square is X, too, because it is equal to the radius of the circle.
The perimeter of the square equals 4 $\times$ X = 4X.
The circumference of the circle is 2 $\times$ $\pi$ $\times$ radius = 2 $\times$ $\pi$ $\times$ X.
Since the circumference of the circle is 15.96 centimeters longer than the perimeter of the square, we can set up the following equation:
2 $\times$ $\pi$ $\times$ X = 4X + 15.96
$\pi$ is about 3.14, so we can plug its value in the equation.
2 $\times$ 3.14 $\times$ X = 4X + 15.96
6.28X = 4X + 15.96
Subtract 4X from both sides.
2.28X = 15.96
Divide both sides by 2.28
X = 7
The length of the radius of the circle is 7 cm.
