Pig on a Rope
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| Pigs may safely graze ... over half the area of the field. |
Maths Challenge: Pig on a Rope
Farmer Hogswell owns a field, which is a perfect equilateral triangle, each side 100 metres long. His prize pig Pigasus is tied to one corner, so that the portion of the field that Pigasus can reach is exactly half the total area.
How long is the rope?
You may – indeed, must – assume that the pig has zero size (which admittedly is pretty silly) and that the rope is indefinitely thin and any necessary knots can be ignored.
How long do you think the rope is? Please post your ideas below, we'll let you know the correct answer next week!
Karen Ramsay-Smith
03 Feb 2012 14:19
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Tags: Challenge Maths
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6 comments by 3 or more people
[Skip to the latest comment]Waleed Khan
The rope is 25(6^0.5) metres long i.e. 61.237metres
08 Feb 2012, 16:06
Karen Ramsay-Smith
Hi Waleed
Thanks for your answer! Unfortunately that’s incorrect. Here’s a clue…
To simplify the problem, make six copies of the field, with six copies of the region accessible to the pig.
Have another go!
08 Feb 2012, 16:36
Nirali Patel
Is the answer the following?
The length of the rope is equal to about 64.30 metres.
08 Feb 2012, 17:44
Vepika Kandjou
I also found 64.30m.
08 Feb 2012, 19:37
Karen Ramsay-Smith
Sorry Nirali and Vepika, that’s not right. Think about the six copies of the field in the shape of a hexagon. Think about the six copies of the region accessible to the pig as a circle inside the hexagon.
No more clues! We will reveal the answer on Monday, keep trying!
09 Feb 2012, 10:33
Karen Ramsay-Smith
Hi guys! We have checked back through this challenge question with our Maths Academic and have found that we are wrong and you are right! The book we took the challenge from is incorrect. So well done all for putting us right! The explanation is here http://blogs.warwick.ac.uk/iggyteam/entry/answer_to_maths_1_2/
13 Feb 2012, 09:10
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