min. Areas, Given Length of Wire for perimeter
A friend and I have tried this question waaaay too long. It's calculus and we cannot solve this dumb question to get the right answer !
Question: A piece of wire 75m long is divided into two pieces. One piece is used to form a circle. The other piece is used to make a square. Find the lengths of the pieces that maximize the total area.
Our work: We have two pieces --> length y and (75-y)
Psquare = (75-y)
side of the square is (75-y)/4
Circum. circle = 2pi(r) , y/2pi=r
Asquare = side^2
You see I did quite a bit of work... basically, I subbed in to minimize the following eq'n:
= (y^2)/4 + ((75-y)^2) /16
and I keep getting weird numbers.
Pleeease, someone tell me what is wrong here because we have checked over and over for hours!