Answer:
r = sqrt(11)
Step-by-step explanation:
Area of sector, A = (theta) r^2/ 2 = 11 cm^2
Perimeter of sector, p= r theta+2r
Length of arc AB, a= r theta
We are given that p = 2a, so equate
r theta + 2r = 2(r theta)
2r = r( theta )
theta = 2 (radians)
Solve for r from area
Area = (theta) r^2 /2 = 11
substitute theta = 2
2 r^2 /2 =11
r^2 = 11
r = sqrt(11)
