675 Words3 Pages

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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