Beyond Pythagoras

... Beyond Pythagoras In this investigation, I shall be studying the relationship between the lengths of the three sides of right angled triangles, their perimeters and their areas. I aim to be able to: -Make predictions about Pythagorean triples -Make generalizations about the lengths of side -Make generalizations about the perimeter and area of corresponding triangles My Table of Results for the Triangles 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 85 185 546 7 15 112 113 240 840 8 17 144 145 300 1224 9 19 180 181 380 1710 10 21 220 221 460 2310 11 23 264 265 552 3036 12 25 312 313 650 3900 13 27 364 365 756 4914 14 29 420 421 870 6090 15 31 480 481 992 7440 16 33 544 545 1122 8976 The reason I used certain triples in my table (for example there is also another triple for 9 as the shortest side which has 12 as the middle side length and 15 as the hypotenuse) is because they followed the pattern I was looking at. Even though some of the other triple combinations might have worked, I chose the ones out of them which went best with the other combinations. The 9,40,41 triple has a difference of 1 between its middle

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