perplexus.info :: Geometry : Fenced In

Fenced In (Posted on 2004-06-18)

A farmer wishes to enclose the maximum possible area with 100 meters of fence. The pasture is bordered by a straight cliff, which may be used as part of the fence. What is the maximum area that can be enclosed?

Submitted by SilverKnight

Rating: 3.7500 (4 votes)

Solution: (Hide)

A circle is the plane figure with highest ratio of area to perimeter. The cliff can be used to bisect a circle of radius 100/pi meters. By symmetry, this will form the pen of largest area. The resulting pen will contain 5000/pi meters squared.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Solution	Dej Mar	2008-11-07 07:42:09
Answer	K Sengupta	2008-11-07 06:08:10
Solution (Assuming...)	wcaexqdz	2004-10-27 12:08:23
Fenced In	Karve Girish	2004-06-20 04:14:00
WAIT A MOMENT	Kevin Tran	2004-06-19 18:27:34
Solution(?)	will	2004-06-19 09:21:18
meters	rixar	2004-06-18 15:48:17
re: More then you think	SilverKnight	2004-06-18 15:05:32
More then you think	Cory Taylor	2004-06-18 14:57:25
re(2): Where did my math go wrong?	Erik O.	2004-06-18 13:28:54
re: Where did my math go wrong?	Charlie	2004-06-18 12:48:03
Where did my math go wrong?	Erik O.	2004-06-18 10:51:31
solution	Charlie	2004-06-18 10:08:07
solution?	Tristan	2004-06-18 10:07:26
Solution	Eric	2004-06-18 09:56:57

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