When zooming in your drawing, your lines are indeed not connected. Maybe you are not familiar enough with the way snap tools can be used.
In your project, since the design is based on several identical entities, it can be efficient to make a bloc for each rectangle, with the reference point in one angle. The rectangle is quickly constructed with the dedicated tool (Rectangle with size, enter your side dim in the boxes).
Then, from the bloc list you can insert copies and position them exactly, using the rotate drop list and "snap intersection", ("auto snap" will also work) to locate the new copy precisely at the corner of the previous one.
You may also draw a temporary square on another layer to help you locate your blocks precisely, layer may then be hidden or deleted. There are often more than one method to achieve your goals...Practicing is the way to learn.
Just keep in mind that precision in CAD has to do with snap tools, you must dig into that if you want to become proficient ( I really recommend Andrew's book if you are not familiar with this kind of software: http://www.qcad.org/en/qcad-documentation
Hers your project with bloc example:
Good luck and come back any time on the forum