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I would think it does a lot of these trucks rust out on the passenger side due to that I recently replaced my floor panels the passenger side was almost completely rusted through a few years before I replaced the heater core
99.99% of the time it does.
I would say if the hoses are new the core nipples may have been moved and cracked at the core and then leak inside.
Also how old is the core? They do get leaks like the radiator does with old age.
Dave ----
I must have clicked on the wrong section on my phone so sorry for that but I'd say its still close to the same. No idea about the core. Probably old. Its a 1993 f150. I'm hoping that's the issue. Between replacing the radiator, the lower hose and topping it off I should have stock in an antifreeze company now then this
We forgive you having post here for the 93 truck but it would be the same thing....heater core.
If you can pressure test the cooling system if it will not hold psi then you can start looking for a leak starting where you see it now, on the floor.
Dave ----
Fortunately you have one of the easiest heater cores there is to replace. Drop the glove box door, remove about six screws holding the cover on, and its right there. I can usually swap them out in under half an hour.