My Math Forum Pythagorean Triple and Right-angled triangles

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 August 2nd, 2007, 07:06 AM #1 Member   Joined: Aug 2007 Posts: 39 Thanks: 0 Pythagorean Triple and Right-angled triangles My maths teacher says that you cannot make a right-angled triangle with a perimeter of 1000m, because according to Pythagoras' theorem, the sides of a right-angled triangle must be a Pythagorean triple. She says that this is impossible with a perimeter of 1000m. However, I found this Pythagorean triple, that gives a perimeter of 1000m. It is: 200² + 375² = 425² When you add the lengths you get: 200m + 375m + 425m = 1000m So, is she wrong? [She has a pHd in mathematics]
 August 2nd, 2007, 07:33 AM #2 Senior Member   Joined: Dec 2006 Posts: 1,111 Thanks: 0 She's right about the fact that the sides of a right triangle must be made up of a Pythagorean triple, and thus that the perimeter of a right triangle must be the sum of the three members of its Pythagorean triple, but it just so happens that she is wrong about the 1000 meter part, because (200, 375, 425) is a Pythagorean triple, and thus the perimeter of the triangle with that particular Pythagorean triple is 1000. However, are you sure that she was referring to all Pythagorean triples, or was she just referring to one particular type of Pythagorean triple, such as primitive Pythagorean triples?

### pythagorean right-angled triangles up to 1000

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