Minimum Fencing

I

Ian McPherson

New member
Joined
Oct 27, 2011
Messages
24
Two equal rectangular lots are enclosed by fencing the perimeter of a rectangular lot and then putting a fence across its middle. If each lot is to contain 1200 square feet, what is the mimimum amount of fence needed to enclose the lots (include the fence across the middle.)


So i drew a picture

Untitled.jpg

And i think that
Perimeter will be 3x + 4y and that the area of just one rectangle is found by xy = 1200.
So i solved xy=1200 to get that y = 1200/x. But i have no idea where to plug that in to, and i cant put it into the perimeter function because I don't know what it's equal to.
 
So think about what you are minimizing...perimeter. You need to get the perimeter in terms of one variable and then take the derivative and then set = 0. So you already solved for y using the area formula. So what can you do with this y = 1200/x equation and the perimeter equation to get it in terms of one variable?
 
oh, take 1200/x and plug it into 3x+4y. so 3x+4(1200/x) will give me x=40, and plugging that into xy = 1200 and get 40y = 1200, giving that y = 30. Therefore you would need 240 feet of fencing :p
 
You must log in or register to reply here.
Top