From what you describe ... your two rectangles are different sizes ... so if you want two of vertices (of A) to become part of surface of B then this maybe what you are after.
For rectangle B the bigger one above rectangle A.
1. Highlite bottom two vertices of Rectangle B, and in vertex mode Vertex---Insert Vertex. Repeat this highlighting the new inserted vertex and one of the original bottom vertices. Snap both inserted vertices to the grid (setting .1 probably works well in your case)
2. Line up these two inserted vertices with the top two vertices of rectangle A.
3. Select the four vertices which are now lined up ... snap to grid.
4. In Object mode: Object->merge, then optimise vertices and surfaces (you should get two vertices removed).
The two rectangles are now welded together.
griff
