Asector of a circle has perimeter 7cm and area 3cm^2. find all possible radii.

Given: 
perimeter of a sector of a circle = 7cm
area of a sector of a circle = 3 cm²

Perimeter of a sector = 2r + l = 2r + rΘ

2r + 2Θ = 7

area of a sector = (Θ/2π) πr² = (Θ/2)r²

(Θ/2)r² =  3  ⇒ Θ = 6/r²

2r + rΘ = 7
2r + r(6/r²) = 7
2r + 6/r = 7

r(2r + 6/r) = r*7
2r² + 6 = 7r
2r² - 7r + 6 = 0
2r² - 4r - 3r + 6 = 0

2r(r - 2) - 3(r - 2) = 0
(2r - 3) (r - 2) = 0

2r - 3 = 0
2r = 3
r = 3/2 or 1 1/2

r - 2 = 0
r = 2

Possible radii are 2 cm and 1 1/2 cm.