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The Goat problem An Investigation

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The Goat Problem The diagram shows a barn in a large field of grass. The barn has a length of 12m and a breadth of 7m. A goat is tied to a stake at the corner of the barn, marked A. The rope used to tether the goat is 17m long. With the aid of a sketch, show the grazing area available to the goat. A Barn Rope=17m 12m 7m Grass

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Would a larger area of grass be available to the goat if it had been tethered to the barn at point B ( midway along the length ) or C ( midway along the breadth) or at any other point on the barn? Investigate ! Exercise:- Repeat the above calculations to find the area available to a goat for grazing, if the barn has a length of 15m, a breadth of 9m and the goat is tethered by a rope of length 23m. B C Barn

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Solution Point A:- Area = 778.33m 2 Point B:- Area = 668.93m 2 Point C:- Area = 743.77m 2

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