### Pythagoras' Theorem.

**Title:**Pythagoras' Theorem.

**Category:**/

**Science & Technology**/Mathematics

**Details:**Words: 1178 | Pages: 4 (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 1178 total…

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…showed last 75 words of 1178 total…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