Loci, How much rope is needed and where do I put the posts?

Calculus
Tutor: None Selected Time limit: 1 Day

A rectangular field measuring 17.5 metres by 10 metres has two posts 7.5 metres apart with a ring on top of each post. The posts are approximately 7 metres from the nearest corners as shown in the diagram. You have two quarrelsome goats and plenty of ropes which you can tie to their collars and you want them to be able to graze the whole field between them. How can you secure them, using the posts, so they can't fight each other, and how much rope is needed?

Need an answer really quickly! If more information is needed (There is a diagram too) go to http://nrich.maths.org/597
Sep 7th, 2015

Thank you for the opportunity to help you with your question!

Thank you for the opportunity to help you with your question!

The solution would be to find a rope that is less than 15m and pass it through both rings and attach the goats at either side.

since approximate distance from the post is 7m. then the rope would need to be 7+7.5m = 14.5m

rope should then be >14.5 but < than 15m


Please let me know if you need any clarification. I'm always happy to answer your questions. Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 7th, 2015

Hello, thank you for the answer, is there anyway you could draw me a diagram (like the one on the website) to show me exactly where to put them and what the circle would look like on my diagram. 

Get back to me as soonyou can!

Sep 7th, 2015

roping problem   roping problem.png 

Sep 7th, 2015

Thanks so much!

Sep 7th, 2015

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