Answer:
[tex]P=\dfrac{\pi r^2+2800}{r} $ ft[/tex]
Step-by-step explanation:
Let the length of the rectangular part =l
The width will be equal to the diameter of the semicircles.
Area of the Skating Rink= [tex]2(\frac{\pi r^2}{2})+(lX2r)[/tex]
Therefore:
[tex]\pi r^2+2lr=2800\\2lr=2800-\pi r^2\\$Divide both sides by 2r\\l=\dfrac{2800-\pi r^2}{2r}[/tex]
Perimeter of the Shape =Perimeter of two Semicircles + 2l
[tex]=2\pi r+2\left(\dfrac{2800-\pi r^2}{2r}\right)\\=2\pi r+\dfrac{2800-\pi r^2}{r}\\=\dfrac{2\pi r^2+2800-\pi r^2}{r}\\=\dfrac{\pi r^2+2800}{r}[/tex]
The perimeter of the rink is given as:
[tex]P=\dfrac{\pi r^2+2800}{r} $ ft[/tex]
