Use science to your advantage.
The word "dinosaur" means "monstrous lizard" (Greek 'deinos' = monstrous + Greek 'sauros' = lizard)
Lizards are reptiles. Reptiles are cold-blooded. That means they depend solely on their environment. They can't regulate their body temperature and must depend on the heat from their environment for warmth. In cold weather, cold-blooded animals hibernate. Hibernation pretty much stops growth. In a warm environment, cold-blooded animals grow faster.
Before the flood, the environment was different. There was no rain. Even man lived longer lives. But after the flood, lifespans began to decrease. If the change in environment affected the lifespan of humans, warm-blooded creatures, then it also affected the lifespan of reptiles.
Another scientific point is that reptiles never stop growing. Now imagine the preflood world. Man lived hundreds of years, compared to the average of 70-90 years today. Reptiles were created just as humans were and if they naturally lived alongside humans, then they would have also lived as long. Imagine a reptile living 500+ years in ideal weather and remember the fact that reptiles never stop growing.
Noah would most likely have taken smaller reptiles on board the ark to save space. Immediately after the flood, these reptiles would have grown and lived fairly long lives, but as their offspring adapted to the environment, the lifespans would have decreased, along with their sizes. If any of the larger reptiles survived they also may have been killed by humans who saw them as a threat.
There's not much mention of the preflood world in the Bible, only that it was wicked. After the flood, there is mention of two beasts that could be dinosaurs, the Behemoth and Leviathan. As far as their demise, the leviathan were killed for food.
Psa 74:14 Thou brakest the heads of leviathan in pieces, [and] gavest him [to be] meat to the people inhabiting the wilderness.
And if any continued to grow large, as I previously stated, they most likely would have been killed because they were seen as a threat.