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GCSE Maths Coursework: Strand 1 - Making and monitoring decisions Equable shapes: The task set is to investigate equable rectangles and further shapes. An equable shape is a shape whose perimeter is 'numerically equal to its area'. Equable Rectangles To start off my investigation I decided to experiment by drawing several rectangles with random lengths and widths. My drawings are included on graph paper. (see page ) I then decided using a table I would investigate every rectangle between that had a width or length between one and ten (whole numbers only). I worked out each shapes area and perimeter and if they were equal I highlighted them: Length Base Area Perimeter 1 1 1 4 1 2 2 6 1 3 3 8 1 4 4 10 1 5 5 12 1 6 6 14 1 7 7 16 1 8 8 18 1 9 9 20 1 10 10 22 2 1 2 6 2 2 4 8 2 3 6 10 2 4 8 12 2 5 10 14 2 6 12 16 2 7 14 18 2 8 16 20 2 9 18 22 2 10 20 24 3 1 3 8 3 2 6 10 3 3 9 12 3 4 12 14 3 5 15 16 3 6 18 18 3 7 21 20 3 8 24 22 3 9 27 24 3 10 30 26 4 1 4 10 4 2 8 12 4 3 12 14 4 4 16 16 4 5 20 18 4 6 24 20 4 7 28 22 4 8 32 24 4 9 36 26 4 10 40 28 5 1 5 12 5 2 10 14 5 3 15 16 5 4 20 18 5 5 25 20 5 6 30 22 5 7 35 24 5 8 40 26 5 9 45 28 5 10 50 30 6 1 6 14 6 2 12 16 6 3 18 18 6 4 24 20 6 5 30 22 6 6 36 24 6 7 42 26 6 8 48 28 6 9 54 30 6 10 60 32 7 1 7 16 7 2 14 18 7 3 21 20 7 4 28 22 7 5 35 24 7 6 42 26 7 7 49 28 7 8 56 30 7 9 63 32 7 10 70 34 8 1 8 18 8 2 16 20 8 3 24 22 8 4 32 24 8 5 40 26 8 6 48 28 8 7 56 30 8 8 64 32 8 9 72 34 8 10 80 36 9 1 9 20 9 2 18 22 9 3 27 24 9 4 36 26 9 5 45 28 9 6 54 30 9 7 63 32 9 8 72 34 9 9 81 36 9 10 90 38 10 1 10 22 10 2 20 24 10 3 30 26 10 4 40 28 10 5 50 30 10 6 60 32 10 7 70 34 10 8 80 36 10 9 90 38 10 10 100 40 A problem that occurred was that some of the shapes in my table that had equal length and base were not rectangles but squares. But squares can be classified as rectangles so my results out of a hundred were accurate the only two rectangles that were equable...

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