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The assignment given is to investigate the relationships between Pythagorean triples (a right angled triangle whose sides satisfy the equation a2 + b2 = c2, where c is the hypotenuse) in the aspects of lengths, area and perimeter.  

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Introduction The assignment given is to investigate the relationships between Pythagorean triples (a right angled triangle whose sides satisfy the equation a2 + b2 = c2, where c is the hypotenuse) in the aspects of lengths, area and perimeter. I have been presented three initial sets of numbers, which shall be used as a guide to form equations. First theses shall be proven to be Pythagorean triples, that is, they satisfy the afore mentioned equation. a2 + b2 = c2 The three triangles given to start with had the dimensions as shown. Also a table was given showing the lengths of the shortest, longest and middle sides of all three triangles along with the area and perimeter of triangle one. Triangle 1 Triangle 2 Triangle 3 (Drawings not to scale) Preliminary Work Below is a table which has been constructed form these initial triangles. There are also some inaccurate formulae which have been drawn...

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