Pythagoras' Theorem.

Title: Pythagoras' Theorem.
Category: Science & Technology / Mathematics
Details: Words: 1449 | Pages: 6.2 (approximately 235 words/page)

Pythagoras' Theorem.

Pythagoras Pythagoras' Theorem is a2 + b2 = c2. 'a' being the shortest side usually the adjacent 'b' being the middle length side usually the opposite and 'c' being the longest side always the hypotenuse. This theorem only works in 'Right angled triangles'. The numbers 3, 4 and 5 satisfy the condition. 32 + 42 = 52 This is because 32 = 9 and 42 = 16, 9 + 16 = 25, and 52 = 25, therefore 32 + 42 = 52. The numbers 5, 12 and 13 and 7, 24 and 25 also satisfy the condition. 52 + 122 = 132 52 = 25 122 = 144 132 = 169 25 (52) + 144 (122 ) = 169 (132 ) 72 + 242 = 252 72 = 49 242 = 576 252 = 625 49 (72) + 576 (242) = 625 (252) Perimeter (3, 4 and 5) 3 + 4 + 5 = 12 Area (3, 4, and 5) ½ x 3 x 4 = 6 Perimeter (5, 12 and 13) 5 + 12 + 13 = 30 Area (5, 12 and 13) ½ x 5 x 12 = 30 Perimeter (7, 24 …showed first 75 words of 1449 total…

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…showed last 75 words of 1449 total…n2 + 22n + 12 22 Now that I know all the formulas using 'n' I can substitute 'n' with 'a'. The formula for 'n' is: 'n = a - 4'. 2 'b = a2 - 1' 4 I got this by knowing that n2 + 4n +3 can be factorised as (n + 1)(n + 3) so using 'a' instead, factorised, it looks like this: (a - 4 - 1)(a - 4 + 1) 2 2 'c = a2 + 1' 4 I got this by just adding 2 onto the formula for 'b'. L is always larger than k 2lk l2-k2 l2+k2

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