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.
