It is known that the perimeter of the sector is 20 cm and the area is 16 square cm. The radius of the sector is calculated

It is known that the perimeter of the sector is 20 cm and the area is 16 square cm. The radius of the sector is calculated

Let the center angle of the circle be θ and the radius be r
c=2πr*θ/2π+2r=r(θ+2)=20
S=πr^2*θ/2π=r^2*θ/2=16
r^2*(20/r -2)/2=16
20r-2r^2=32
r^2-10r+16=0
(r-2)(r-8)=0
R = 2 or r = 8
R = 2 θ = 8 > 2 π rounding off
r=8cm

It is known that the radius of a sector is 6cm, and the perimeter is 20cm

The arc length L = 20-6 * 2 = 8 is obtained
Area s = LR / 2 = 8 * 6 / 2 = 24
So the sector area is 24 cm square

Given that the perimeter of the sector is 20cm and the area is 16cm2, what is the radius of the sector?

Let the radius be r and the center angle be α
2r+πr·α/180=20
πr²·α/360=16
The solution is r = 2 or r = 8