From the given diagram, let's find the length of the park's boundary.
We can see the side of the park's boundary is a circular arc and the top and bottom are the bases of triangles.
To find the length of the circular sides, apply the length of arc formula:
[tex]arc\text{ length=}2\pi r\ast\frac{\theta}{360}[/tex]
Where:
Θ = 120 degrees
π = 3.14
radius, r = 50 yards
Hence, we have:
[tex]\text{arc length=2}\ast3.14\ast50\ast\frac{120}{360}=104.67\text{ yards}[/tex]
This means the length of one circular side of the boundary is 104.67 yards.
We have two circular sides of the boundary.
The top and bottom sides form equilateral traingles.
Hence, the length of the top and bottom sides are 50 yards each.
To find the total length of the boundary, we have:
Total length = 104.67 + 104.67 + 50 + 50 = 309.34 yards
Rounding off to the nearest yard, the length of the park's boundary is:
309 yards
ANSWER:
D. 309 yards
