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# The fencing problem.

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Introduction

Maths Coursework I am going to carry out this investigation. I have realised that I must investigate the following shapes: * Squares * Rectangles * Triangles * Circles * Parallelograms * Polygons * Hexagons My interpretation of the question: "There is ONLY 1000m of fence, and therefore she needs to have a perimeter of 1000m, however this shape must have the biggest possible area". ...read more.

Middle

Rectangles L (m) W (m) Perimeter (m) Area (m2) 100 400 1000 40000 200 300 1000 60000 150 350 1000 52500 125 375 1000 46875 250 250 1000 62500 The graph shows how as the length increases the area increases, and there it shows the maximum area for a rectangle of perimeter 1000m. ...read more.

Conclusion

area = 1/2 base x perpendicular height 2. area = 1/2 ab sin c 3. area = square root of ( s(s-a)(s-b)(s-c)) Equilateral Triangle Side = 333.3 Perimeter = 1000m Area = 1/2 ab sin c = 1/2 333.3 x 333.3 sin 60 = 48059.60347 This is the maximum area of an equilateral triangle and therefore the square has still the maximum area, for a perimeter of 1000m. Gurpal Gahir 11M ...read more.

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