A Right Angled Triangle With Sides in Arithmetic Progression

The 3-4-5 triangle is familiar to anyone who has studies Pythagoras Theorem, This triangle is the smallest right angled triangle. The sides are in an arithmetic progression with first term 3 and common difference 1. Are there any other right angled triangles with sides in an arithmetic progression?




\[x+k=0 \rightarrow x=-k\]
\[x-3k=0 \rightarrow x=3k\]
This means that the sides of the triangle are
\[3k, \:4k, \: 5k\]
- the triangle is just a scaled up 3-4-5 triangle.

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