A sector 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.