... right-angled triangle: The perimeter and area of this triangle are: Perimeter = 3 + 4 + 5 = 12 units Area = 1/2 x 3 x 4 = 6 square units The table below shows the area and perimeter of the (5, 12, 13) and (7, 24, 25) right-angled triangles. 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 To work out the perimeter I added all the sides together, and to get the area I multiplied the shortest length with the middle length then divided it by 2. (3, 4, 5); (5, 12, 13) and (7, 24, 25) are all called Pythagorean triples because they satisfy the condition: a² + b² = c² Below is a table, which shows the next results in the sequence: 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 15 112 113 240 840 17 144 145 306 1224 19 180 181 380 1710 21 220 221 462 2310 23 264 265 552 3036 The shortest length increases by two each time, as they are all odd numbers. I have also noticed that the middle length increases by ...

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