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  • Level: GCSE
  • Subject: Maths
  • Word count: 1605

Beyond Pythagoras

Extracts from this document...

Introduction

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 ...read more.

Middle

and the length of the hypotenuse. I will also work out a formula for the area and the perimeter of the triangle. By taking the date from the "beyond Pythagoras "sheet and the data on the excel sheet I can work out the formula by using a a sequence diagram to find a constant and then using a linear equation if it there is a constant on the second step or a quadratic if there is a constant on the third step. I this is how I will work out the formula for the shortest side of family 1 X Y 1 3 > 2 2 5 > 2 3 7 There is a constant on the second step so I can solve it with a linear equation. I will solve it using the standard linear equation Y = ax + c I will put the numbers into this equation so I can work out the formula. A * 1 + c = 3 (i) A * 2 + c = 5 (ii) I will then take "ii" from "i" to find out what a is = 2 I will then put this into "i" to find out what "c" is 2 + c = 3 (i) I have to take 2 from three C = 1 Y = 2 * x + 1 X is the sequence number Checks 2 * 1 + 1 = 3 ...read more.

Conclusion

2 * x + 1 + Y = 2x2 + 2x + Y = 2x2 + 2x + 1 = (c)nick Peplow Y = 4x2 + 6x + 2 It will give the perimeter. Checks Y = 4 * 12 + 6 * 1 + 2 = 12 Y = 4 * 22 + 6 * 2 + 2 = 30 Y = 4 * 32 + 6 * 3 + 2 = 56 By checking I have found that my formula is correct. Now I need to find the area The formula for finding the area of a triangle is 1/2 base * height So in need to divide the formula for "b" by two and then times it by the formula for "a" This is the formula for "b" Y = 2x2 + 2x (i) And this is the formula for "a" Y = 2 * x + 1 (ii) So basically all you have to do is divide the formula that you get from "i" And then times it by "ii" Y = (2x2 + 2x) /(divided) 2 * (2x + 1) Check Y = (2*12 + 2*1) / 2 * (2*1 + 1) =6 Y = (2*22 + 2*2) / 2 * (2*2 + 1) =30 Y = (2*32 + 2*3) / 2 * (2*3 + 1) =84 By checking my formula I have proved that it is correct. (c)nick Peplow (c)Nick Peplow ...read more.

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