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Fencing problem.
Member rating: No Rating | Words: | Submitted: Fri Feb 13 2004
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Introduction A farmer has 1000m of fencing to fence an area of land. She doesn't mind what shape the fenced land takes but she wants to have the biggest possible area. I will use my mathematical skills to work out this maximum area using shapes such as: Triangles: Isosceles Right Angle Scalene Quadrilaterals: Rectangles Trapeziums Parallelograms Polygons: Pentagons Hexagons Decagons etc Semi-Circles Circles Triangles Isosceles Area (a) =1/2 x base x height= 1/2bh To work out the area of an isosceles triangle you have to work out the length of the sides. 1000 = 50 + 2k 2k = 1000 - 50 2k = 950 k = 950/2 k = 475m To then find the height (h) you have to cut it in half, giving you two right-angle triangles: 2 2 2 h + 25 = 475 2 2 2 h =475 - 25 Therefore h = (sqrt) square-root 225625-625 h = 474.342 Therefore to find the area: Area (a) =1/2 x base x height = 1/2bh A = 1/2 x 25m x 474.342 = 2 A = 11,858.541 (m) Next is a...
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