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An infinite number.

Working only with the 3,4,5 triangle, you get:

(*2) 6,8,10 or

(*3) 9,12,15 or

(*4) 12,16,20 or

(*5) 15,20,25 etc for ever.

And, apart from that, there are an infinite number of starting triplets (5,12,13) is the next smallest one.

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Q: How many right-angled triangles have lengths with whole numbers?
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