All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Shapes
The art of fencing (Posted on 2006-12-27) Difficulty: 5 of 5
Three neighbours buy a piece of land that they want to cultivate as a garden. The land has the shape of a square. To avoid that their petunias and pumpkins get in the way of each other, they decide to split the garden into three cells of equal area. To keep things simple, the border between two adjacent cells should be a straight line. Under these constraints, can you help them to divide their garden such that the total length of the fence is minimized? How would you divide the garden for five, six, seven or eight neighbours?

No Solution Yet Submitted by JLo    
Rating: 3.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts idea | Comment 5 of 6 |
this seems to be an optimazation problem where a constraint equation is necessary and the surface area of the plot of land ( amt of total fencing) needs to be minimized namely through differentiation.

Perhaps you could say A=xy

min s(a)= 2x + 4y

substituting s(a)= 2x + 4A/x

the next step would be to take a derivative and see if there is indeed a minimum however a value for A ( area of the land) is not given to us so

  Posted by alex on 2007-08-19 00:49:30
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information