If the sides of a right angled triangle are in $AP$, then the sides are proportional to 

Let the sides of triangle are $(a-d),a_1(a+d)$.

By Pythagoras theorem, we have

$\begin{array}{l}(a+d{)}^2=a^2+(a-d{)}^2\\ \Rightarrow a^2+d^2+2ad=a^2+a^2+d^2-2ad\\ \Rightarrow a^2=4ad\\ \Rightarrow a=4d\end{array}$

So, tile sides are $3d, 4d, 5d.$

Hence, the sides are proportional to 3 : 4 : 5.