+-40 a sector AOB of a circle with centre O and radius r cm . the angle AOB is θ radians. the area of the sector is 12cm^2 . the perimeter of the sector is 4 times the length of the arc AB
find the value of r
+128460 Area of sector = (1/2) r^2 * θ
12 = (1/2) r^2 * θ
24 = r^2 * θ
The perimeter of the sector = 2r + arc length of AB
4 arclength AB = 2r + arclength AB
3arclength of AB = 2r divide both sides by 3
arclength of AB = (2/3)r
And the arclength of AB = r * θ
So
r * θ = (2/3)r ( divide out r ) ⇒ θ = (2/3) rads
So
24 = r^2 * (2/3)
24 (3/2) = r^2
72 / 2 = r^2
36 = r^2 take the square root of both sides
6 (cm) = r
