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By Lyndon Robertson Maths 10x1 Task 13 Beyond Pythagors Mathematics Gcse The numbers 3,4 and 5 satisfy the condition 3²+4²=5² because: 3²=3x3=9 4²=4x4=16 5²=5x5=25 and so 3²+4²=9+16=25=5² 1) The numbers 5, 12 and 13 satisfy the condition 5²+12²=13² because: 5²=5x5=25 12²=12x12=144 13²=13x13=169 and so 5²+12²=25+144=169 b) The numbers 7, 24 and 25 satisfy the condition 7²+24²=25² because: 7²=7x7=49 24²=24x24=576 25²=25x25=625 and so 7²+24²=49+576=625=25² Perimeter and area of the right-angled triangles 2) a) Perimeter and area of (5,12,13) triangle: Perimeter = 5+12+13 = 30 Area = 5 x 12 ÷ 2 = 30 Perimeter and area of (7,24,25) triangle: Perimeter = 7+24+25 = 56 Area = 7 x 24 ÷ 2 = 84 Length of shortest side Length of middle side Length of longest side Perimeter Area 1 3 4 5 12 6 2 5 12 13 30 30 3 7 24 25 56 84 4 9 40 41 90 180 In the first table there was only a difference of 1 between the length of the middle side and the length of the longest side. The (smallest number) ² + (middle number) ² = (largest number) ². N 1 2 3 4 3 5 7 9 2 2 2 The short side formula is 2n+1, the difference between...

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