The perimeter of a quarter circle is given by the formula P = (pi/2)*r + 2r, where P is the perimeter, r is the radius, and pi is approximately 3.14159.
Given that the perimeter of the quarter circle is 5.712 feet, we can substitute this value into the equation and solve for r:
5.712 = (pi/2)*r + 2r
Rearranging this equation, we get:
5.712 = (pi/2 + 2)*r
Dividing both sides by (pi/2 + 2), we get:
r = 5.712 / (pi/2 + 2)
Using the value of pi approximately equal to 3.14159, we get:
r = 0.873 feet (rounded to three decimal places)
Therefore, the radius of the quarter circle is approximately 0.873 feet.