I am quite sure this question was a result of misguided information presented to the OP about Special relativity. But I think the OP only wanted a thought-experiment kind of proof for length contraction. The fact that they thought time dilation causes length contraction is to some extent irrelevant.
When I presented an edit to this effect, it was rejected. So are we going to keep down-voting this question and not allow more answers to show up in the true intent of the OP?