The T-REX and Giant Penny

I really need some expert help on this.

I don't remember the dinosaur and the giant penny being in the first comic (although my memory is bad and I don't believe I have the book anymore to check), however I do remember Superman fighting the giant dinosaur in the sequel comic, "the Dark Knight Strikes Again".

My question is, assuming that the T-Rex is in both books, where did it come from?

I am not a hardcore follower of the batman story,especially in recent years, but I find it weird that Batman would keep a giant robotic T-Rex in his batcave.

I'm sure it would come in handy for fighting... something, but I really just want to know if anybody knows the back story of where it came from.

If you guys know anything about the giant penny as well please also share.

Thanks,

sublbc