caption: Starter You may have noticed last lesson that sometimes all three sides of the right-angled triangle were integers.
exif: {"Image DocumentName": "Starter You may have noticed last lesson that sometimes all three sides of the right-angled triangle were integers.", "Image ImageDescription": "These are known as Pythagorean triples. For example: The sides could be 20, 21 and 29, as = 29 2 and thus satisfy Pythagoras\u2019 Theorem. How many Pythagorean triples can you find (3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25) (20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53) (11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73) (13, 84, 85) (36, 77, 85) (39, 80, 89) (65, 72, 97) Note that you could also have any multiple of any of these triples as the triangles could be scaled in size. So for example (3, 4, 5) could become (6,8,10) and so on. A final note is that if you changed the powers from 2 to 3, or any higher number, then there would never be any solutions. This is known as Fermat\u2019s Last Theorem, which was unproven for hundreds of years before being proven in 1995.", "Image XResolution": "300", "Image YResolution": "300", "Image ResolutionUnit": "Pixels/Inch", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}