Mathematical Investigation
We have been given five different pieces of information for three
different triangles and we are trying to find any similarities or
differences between this family of triangles (Pythagorean triangles).
We want to try and see if this works only for Pythagorean triangles or
if it works with other triangular families. I have decided to put it
into a table, so that I can then compare the relationships and try to
find the nth term for the shortest side, middle side, hypotenuse, area
and the perimeter.
N
Shortest side (s)
Middle side (m)
Hypotenuse (h)
Area (a)
Perimeter (p)
1
3
4
5
6
12
2
5
12
13
30
30
3
7
24
25
84
56
4
9
40
41
180
90
5
11
60
61
330
132
6
13
84
85
546
182
7
15
112
113
840
240
Finding the shortest side:
I have become aware of the fact that in the column showing the
shortest side the numbers increase by two each time, showing a
pattern, it can't be the two times
Table because all of the numbers are odd but they must have something
to do with the two times table:
N
(s)
×2
1
[IMAGE]3
2
2
5
4
3
[IMAGE]7
6
4
9
8
The rule therefore must be: 2n + 1 because they are all one away from
the two times table so you just need to add one.