# Pythagoras Experiment

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Pythagoras Experiment Aim: To investigate the relationships between the lengths of the 3 sides of the right angled triangles and the perimeters and areas of these triangles. Task 1: a) The numbers 5, 12, 13 satisfy the condition. 5² + 12² = 13² Because 5² = 5x5 = 25 12² = 12x12 = 144 13² = 13x13 = 169 And so 5² + 12² = 25 + 144 = 169 = 132 b) The Numbers 7, 24, 25 also satisfy the condition. 7² + 24² =25² Because 7² = 7x7 = 49 24² = 24x24 = 576 25² = 25x25 = 525 And so 7² + 24² = 49+ 576 = 625 = 25² Task2: The perimeter and area of the triangle are: Perimeter = 5 + 12 + 13 = 30 units Area = ½ x 5 x 12 = ½ x 60 = 30 square units a) 5 12 13 [IMAGE] b) 24 7 25 [IMAGE] Perimeter = 7 + 24 + 25 = 56 units Area = ½ x 7 x 24 = ½ x 168 = 84 square units [IMAGE] 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 84 84 Task3: Length of short side is going to be in fixed steps meaning that this is a linear sequence and the length of middle side and longest side is actually a quadratic sequence because they are not in fixed steps and in geometric sequence. 4 , 12 , 24 , 40 [IMAGE]