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Beyond Pythagoras Introduction: a² + b² = c² The numbers 3, 4 and 5 can be the lengths of the sides of a right-angled triangle. The perimeter = a + b + c The area = a × b ÷ 2 The numbers 5, 12 and 13 can also be the lengths of the sides of a right-angled triangle. This is also true for 7, 24 and 25. These numbers are all called Pythagorean triples because they satisfy the condition. Aim: I am going to investigate the different values of a, b and c for which the formula a² + b² + c² works. I will also investigate the even and odd values for (a) for which the formula works. I also intend to find out a relationship between a, b and c and their perimeters and areas. The rules for my first Pythagorean triples are: 1. (a) Must be a odd consecutive number 2. (b) Must...

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