# Optimization (ii)

• Apr 4th 2007, 02:57 PM
r_maths
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 semi-circular 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
• Apr 4th 2007, 03:28 PM
Soroban
Hello, r_maths!

Quote:

A semi-circular window of radius r cm is divided into sectors, each of area 125 cm²
http://img208.imageshack.us/img208/5...ewiz008ha2.jpg
Show that the perimeter of each sector is: .P .= .2(r + 125/r)

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)

• Apr 5th 2007, 02:34 AM
r_maths
Thanks :)