Can we find two non-congruent right triangles with whole-number lengths

Trevor Wood

Trevor Wood

Answered question

2022-05-25

Can we find two non-congruent right triangles with whole-number lengths and congruent hypotenuses?

Answer & Explanation

Amelie Douglas

Amelie Douglas

Beginner2022-05-26Added 8 answers

Let ( a 1 , b 1 , c 1 ) and ( a 2 , b 2 , c 2 ) be arbitrary non-proportional pythagotrean triples, and let d := g c d ( c 1 , c 2 ). Then
c 2 d ( a 1 , b 1 , c 1 ) , c 1 d ( a 2 , b 2 , c 2 )
are pythagorean triples to noncongruent right triangles with the same hypotenuse c = c 1 c 2 d .

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