How do we solve this?

Question

The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector

Answer 1

Question asks to find   s = f (A_S )    A_S = area of the sector   s = arc length = 2r => central angle (θ) = 2 radians

A_S =  [ θ / 2π ] π r²  =  r²   =>  A_S = r²    thus     r = √A_S

s = 2r = 2 √A_S

s = f (A_S )

s = 2 √A_S

Answer 2

A = r² θ / 2          area of sector

2A = r² θ

2A / θ = r²

√(2A / θ) = r

length of arc - 2√(2A / θ)