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# Beyond Pythagors

• Essay length: 1235 words
• Submitted: 21/08/2003
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GCSE Fencing Problem

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Beyond Pythagors

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.

The numbers 3, 4 and 5 satisfy this condition

32 + 42 = 52

because 32 = 3 x 3 = 9

42 = 4 x 4 = 16

52 = 5 x 5 = 25

and so 32 + 42 = 9 + 16 = 25 = 52

The numbers 5, 12, 13 and 7, 24, 25 also work for this theorem

52 + 122 = 132

because 52 = 5 x 5 = 25

122 = 12 x 12 = 144

132 = 13 x 13 = 169

and so 52 + 122 = 25 + 144 = 169 = 132

72 + 242 = 252

because 72 = 7 x 7 = 49

242 = 24 x 24 = 576

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