How did short sword helped Romans army?

I dont know, maybe the Romans were too lazy :)

But to answer your question, the Romans already thought that their spears were long enough to jab their opponents. So they thought their sWords should be short for close range, the opponent about 2-4 feet away from them.

Another theory is that they used to knock their opponents with their shield so that the opponent becomes dizzy or unaware of whats going on, so that the Romans have the opportunity to jab them freely. This only happens when the opponent gets too close to him.