Most dinosaurs - including the T-Rex - died at a very young age. Growth rings preserved in the fossils of various types of dinosaurs indicate that even giant species typically died before the age of 30.
Part of the explanation may be their incredibly fast growth, fueled by a high metabolism, unlike typical reptiles today. Some reached their full size in only 3-5 years, compared to today's large mammals, which mature over years. This rapid maturation, combined with high-frequency culture, led to a high-paced life.