Question Number 103171 by bemath last updated on 13/Jul/20

Commented bybobhans last updated on 13/Jul/20

(2a) a sector of a circle with radius r has  perimeter 20 units and area 21 square  units . Find all possible of r and the   corresponding value of θ .

Answered by bobhans last updated on 13/Jul/20

perimeter = 2r + θr   20 = 2r+θr ⇒θ = ((20−2r)/r)...(1)  area = (1/2)θr^2   21= (1/2)θr^2  ...(2)  (1) and (2) ⇒ 42 = (((20−2r)/r)).r^2   42 = 20r−2r^2  ⇒ r^2 −10r+21 = 0  (r−3)(r−7) = 0  { ((r = 3 unit)),((r=7 unit)) :}  for r = 3 unit ⇒θ=((20−6)/3) = ((14)/3) radian  for r = 7 unit ⇒θ=((20−14)/7) = (6/7) radian