Here is a table showing the number of tiles used possibilities down the left column and then the types of slopes of the sides that produce those number of tiles inside the rectangle.
The meaning of the three numbers arre as follows,
So if the rectangle were as follows;
The shortest side (red) is $3$ across and $2$ up and just one length of that slope so $3,2,1$
but the other side (green) is two of that length so its $3,2,2$) . On the table above it show that $26$ tiles are needed for $3,2,2$.