Answer:
[tex]P = (20 + 4\pi) \text{ ft}[/tex]
[tex]P\approx 32.57\text{ ft}[/tex]
Step-by-step explanation:
We can see that the perimeter of the pool has the following components:
- 3 sides of the rectangle
- circumference of the semicircle
We can model this with an equation, knowing the circumference of a circle formula:
where [tex]d[/tex] = diameter:
[tex]P = 6 + 8 + 6 + \dfrac{1}{2}\pi d[/tex]
We can identify the diameter as the same as the long side of the rectangle, which is 8. Thus, the equation becomes:
[tex]P = 6 + 8 + 6 + \dfrac{1}{2}\pi(8)[/tex]
Simplifying, we get:
[tex]\boxed{P = (20 + 4\pi)\text{ ft}}[/tex]
We can approximate this using a calculator:
[tex]\boxed{P\approx 32.57\text{ ft}}[/tex]
