Question

A sector has angle 2.5 radians and perimeter of 18cm. find the radius of the sector

(The answer is 10.5, but how?) pls help

Answer 1

4 cm

Explanation:

Perimeter = 18cm

θ = 2.5 radian

s = rθ, s = Arc length

Perimeter of Sector, P = arc length, s + 2r

Perimeter = rθ + 2r

r = Radius

18cm = r(2.5) + 2r

18cm = 2.5r + 2r

18cm = 4.5r

r = 18 /4.5

r = 4