
Optimization (ii)
Once again this question isn't really optimization but the second part is (which I know how to do). Its the first part i'm stuck at.
A semicircular window of rcm is divided into sectors, each of area 125cm^2
http://img208.imageshack.us/img208/5...ewiz008ha2.jpg
Show that the perimeter of each sector is P = 2(r + 125/r)
Thanks

Hello, r_maths!
The perimeter is: .P .= .2r + s, where s is the arclength.
Since arclength is given by: .s .= .rθ, where θ is the central angle,
. . we have: .P .= .2r + rθ .[1]
The area of a sector is given by: .A .= .½r²θ
So we have: .½r²θ .= .125 . → . θ = 250/r² .[2]
Substitute [2] into [1]: .P .= .2r + r(250/r²) .= .2r + 250/r
Therefore: .P .= .2(r + 125/r)
