Answer:
52.02 ft
Step-by-step explanation:
If the golf hole is round, it is a circle. Given the area of the circle, we can determine the perimeter (circumference) of the circle.
The area (A) of a circle is given by:
[tex]\boxed{ \begin{array}{ccc} \text{\underline{Area of a Circle:}} \\\\ \text{A} = \pi r^2 \\\\ \text{Where:} \\ \bullet \ A \ \text{is the area of the circle} \\ \bullet \ r \ \text{is the radius of the circle} \end{array}}[/tex]
Given that the area is 216 square feet, solving for the radius (r):
[tex]\Longrightarrow 216 \text{ ft}^2=\pi r^2\\\\\\\\\Longrightarrow r = \sqrt{\dfrac{216 \text{ ft}^2}{\pi}}\\\\\\\\\therefore r \approx 8.29 \text{ ft}[/tex]
The circumference (C) of a circle is given by:
[tex]\boxed{ \begin{array}{ccc} \text{\underline{Circumference of a Circle:}} \\\\ \text{C} = 2\pi r \\\\ \text{Where:} \\ \bullet \ C \ \text{is the circumference of the circle} \\ \bullet \ r \ \text{is the radius of the circle} \end{array}}[/tex]
[tex]\Longrightarrow C = 2\pi(8.29 \text{ ft})\\\\\\\\\therefore C \approx \boxed{52.08 \text{ ft}}[/tex]
Therefore, the perimeter (circumference) of the round golf hole is approximately 52.08 feet.