Lower Radiator hose question

Having some heating issues at highway speeds, I can drive in the city or in parade for that matter and it can run all day, but when I get on highway 60-70 mph for 30 minutes or so it starts climbing .....so now I'm going through the elimination process.
The question I have ...Right now anyway ..... is on the lower radiator hose, I bought a new one and it looks like it has to be cut off about 1/2 inch or so where it goes on the water pump so it will line up with the radiator.
... Is this normal ? I would think it should just be the right length. Anyone else run into this. My old hose that is on the car looks as if it has been cut also.

Radiator has been Rodded out cleaned .....for a different reason...... thermostat is/was fairly new I have changed that and was going to replace hose again, first hose replacement didnt work out so well after cutting ....... the hose I just bought looks like the one I screwed up, so the old one is back on car. Should the hose be cut to fit? ...... oh ya, this is on a 72 Dodge Demon 340