A garden is to be designed in the shape of a circular sector, with radius r and central angle theta. the garden is to have a fixed area A. for what value of R and theta will the length of the fencing be minimized?

Answer 1

the fence length

f = 2r + rθ

since the area is constant,

1/2 r^2 θ = A
θ = 2A/r^2

so,

f(r) = 2r + 2A/r

Now just find r where df/dr = 0
Use that to get θ