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Beyond Pythagoras The aim of this investigation is to investigate Pythagoras theorem and to find a formula for the shortest side, middle length, hypotenuse, area and perimeter. Because I have typed this up on a computer... ^ is squared * is times / is divided Pythagoras is A2 + B2 = C2 I am going to prove this theory be finding out if the following numbers adhere to the rule. Triangle 1 5 12 13 5^ + 12^ = 13^ 5^ = 5*5 = 25 12^ = 12*12 = 144 13^ = 13*13 = 169 So 5^ + 12^ = 25 + 144 = 169 = 25^ The perimeter of the triangle is All the lengths of the side added up 5 + 24 + 25 = 30 The area of the triangle is 1/2 base * height 1/2 * 12 * 5 = 30 Triangle 2 7 24 25 7^ + 24^ =25^ 7^ = 7*7 = 49 24^ = 24*24 = 576 25^ = 25*25 = 625 So 7^ + 24^ = 49 + 576 = 625 = 25^ The perimeter of the triangle is All the lengths of the side added up 7 + 24 + 25 = 56 The area of the triangle is 1/2 base * height 1/2 * 24 * 7 = 84 Length of shortest side Length of middle side Length of longest side Perimeter Area 3 4 5 12 6 5 12 13 30 30 7 24 25 56 84 9 40 41 90 180 11 60 61 132 330 13 84 85 182 546 15 112 112 239 840 17 144 144 305 1224 Please find enclosed "sheet 1" To create this I used excel to find the Pythagorean triangles Basically I created one horizontal line of numbers going up one at a time and another vertical line the same. I used the formula =B1+1 (the cell B1 has a...

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