Answer:
Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.
Explanation:
The perimeter of the sector is equivalent to the length of the rope which is 18 meters
Perimeter of the sector= 2 x radius + length of the arc
But length of arc= radius x central angle in radian
18= 2(3.5)+ 3.5(central angle in radians)
18=7+3.5 (central angle in radians)
18–7=3.5(central angle)
11=3.5(central angle)
central angle =11/3.5=3.14 radians or pi radians
Angle in degrees =pi radians x 360 degrees/2pi radians =pi radians x 180 degrees/pi radians = 180 degrees
Therefore the central angle = 180 degrees because pi radians is half of 2pi radians which is half of 360 degrees
Notes: This sector shape is a semicircle because the central angle is 180 degrees
Check: Length of Arc for semicircle =3.5(pi radians)=11 meters
Perimeter of the sector = 2r + length of arc= 2(3.5)+11= 7+11=18 meters exactly the length of the rope.