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.
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
252 = 25 x 25 = 625
and so 72 + 242 = 49 + 576 = 625 = 252
3 , 4, 5
Perimeter = 3 + 4 + 5 = 12
Area = ½ x 3 x 4 = 6
5, 12, 13
Perimeter = 5 + 12 + 13 = 30
Area = ½ x 5 x 12 = 30
7, 24, 25
Perimeter = 7 + 24 + 25 = 56
Area = ½ x 7 x 24 = 84
From the first three terms I have noticed the following: -
• 'a' increases by +2 each term
• 'a' is equal to the term number times 2 then add 1
• the last d...