I shall retrieve simple information regarding these triangles. Once I have found these I shall place all my information into tables:

¤ Area of the shape (½ ab= area² )

After I have retrieved the information I shall interrogate the table in order to find patterns and formulae. Once I believe that I have found all the formulae for the preliminary problem and have proven algebraically that they work, only then will I move onto an extension task.

In the extension task I hope to see patterns in different families of Pythagorean triples such as:

I shall also look into the 3, 4, 5 rule and see whether all triples are a basis of these or just some of them are.

“n” Small Medium Large Perimeter Area

2x2 + 2xy + y2 = x2 + 2xy + 2xy + 4y2

Also if you do as above but subtract one you get b

Some topics in this essay:
Pythagorean Theorem, A² D², Quadratic Rule, Length Hypotenuse, PROVES TRUE, Medium Perimeter, Pythagorean Triples, Perimeter Shape, , = 4, A²+ B², 3 4, 4 5, 3 4 5, + 1, + 2xy +, finding formula, y2 =, 1 =, + 2xy, 2xy +, + y2 =, + y2, + 8n³ +, 4n^4 + 8n³,