Pythagoras' Theorem

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Pythagoras' Theorem I am going to study Pythagoras' theorem. Pythagoras Theorem is a2 + b2 = c2. 'a' being the shortest side, 'b' being the middle side and 'c' being the longest side (hypotenuse) of a right angled triangle. For example, I will use 32 x 42 = 52 . This is because: 32 = 3 x 3 = 9 42 = 4 x 4 = 16 52 = 5 x 5 = 25 So.. 9 +16 = 25 For this table, I am using the term a, b, b + 1 Triangle Number (n) 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 5 11 60 61 132 330 6 13 84 85 183 546 7 15 112 113 240 840 8 17 144 145 296 1224 Formulas ======== Shortest side = 2n + 1, n being the triangle number Middle side = 2n2 + 2n. This is because: Triangle Number 1 = 2 x 2 2 = 3 x 4 3 = 4 x 6 4 = 5 x 8 = 2n2 + 2n 5 = 6 x 10 6 = 7 x 12 7 = 8 x 14 8 = 9 x 16 Longest side = 2n2 + 2n + 1 Perimeter = A + B + C Area = A x B x 0.

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