A Right Angled Triangle With Sides in Arithmetic Progression
\[x+2+(x+k)^2=(x+2k)^2\]
\[x^2+x^2_2kx+k^2=x^2+4kx+4k^2\]
\[x^2-2kx-3k^2=0\]
\[(x+k)(x-3k)=0\]
Hence
\[x+k=0 \rightarrow x=-k\]
or \[x-3k=0 \rightarrow x=3k\]
.This means that the sides of the triangle are
\[3k, \:4k, \: 5k\]
- the triangle is just a scaled up 3-4-5 triangle.