Area that the animal can graze is 4840 * 9 / 2 acres (4840 yd^2 = 1 acre; 9 ft^2 = I yd^2)
Area that the animal can graze = pi * r^2 / 6 (one sixth of a circle) Equating the two and solving for r gives r = sqrt ((4840 * 9 * 6) / (pi * 2)) = 67.985 ft (approx) _____ From: [email protected] [mailto:[email protected]] On Behalf Of John M. Steele Sent: 01 January 2010 21:56 To: U.S. Metric Association Subject: [USMA:46344] Re: A puzzle from the UAE So the animal can graze 0.5*0.5 = 0.25 acre. The only pertinent feature of the equilateral triangle is the 60° apex where the animal is tied.. It can graze a 60° arc of a circle of some unknown radius, r. (pi/6)*r² = 43560 ft²/4 Disobeying instructions and working to surveying standards, r = 144.22 ft. If the (half) acre is Survey, so are the feet' otherwise International. For extra credit, it won't be EXACTLY the same problem, but it can be metricated by using a 0.2 ha triangle, in which case the goat can graze 1000 m², on a rope of length 43.702 m _____ From: Pat Naughtin <[email protected]> To: U.S. Metric Association <[email protected]> Sent: Fri, January 1, 2010 3:45:08 PM Subject: [USMA:46341] A puzzle from the UAE Dear All, This puzzle comes from the United Arab Emirates (UAE) that finally changed its petrol pumps from (UK) gallons to litres yesterday leaving the USA as the only remaining supplier of fuel to the public in (USA) gallons. See: http://www.uaeblogging.com/2009/12/the-end-is-nigh-3 Here's the puzzle: In a field the shape of an equilateral triangle whose area is half an acre, there is an unspecified grazing animal. The beast is attached to one corner of the field by a rope, so that it can graze exactly 50% of the area of the field. To the nearest foot, how long is the rope? Show your working. (You can ignore those parts of the rope around the animals neck, around the post and making the knots, and you can assume as zero the distance between the rope and the animals mouth. Its a straightforward geometry puzzle with no tricks.) I assume that changing the acre to square metres and the rope length to metres or millimetres is not permitted! Cheers, Pat Naughtin Author of the ebook, Metrication Leaders Guide, that you can obtain from http://metricationmatters.com/MetricationLeadersGuideInfo.html PO Box 305 Belmont 3216, Geelong, Australia Phone: 61 3 5241 2008 Metric system consultant, writer, and speaker, Pat Naughtin, has helped thousands of people and hundreds of companies upgrade to the modern metric system smoothly, quickly, and so economically that they now save thousands each year when buying, processing, or selling for their businesses. Pat provides services and resources for many different trades, crafts, and professions for commercial, industrial and government metrication leaders in Asia, Europe, and in the USA. Pat's clients include the Australian Government, Google, NASA, NIST, and the metric associations of Canada, the UK, and the USA. See http://www.metricationmatters.com/ to subscribe.
