I remember a quick real world example for this rule. I think it was mentioned in this forum before.
Take three toothpicks, can you make a triangle out of them? (I should hope so)
Now take two toothpicks and a meter stick, can you get the two toothpicks to stretch ALL the way over to touch both ends of the meter stick, the answer is you can't. A side can't be bigger than the two other sides put together