Is working out at 15 years old good for the teenagers body?

Teens and exercise. Exercise (of some sort) is good for everyone. Teenagers can benefit from doing cardio work, like running, biking, stairmaster, or elliptical, and can do weight training, not weightlifting. In weight training, it's lower weights but more reps. This decreases the risk of injury to the musculoskeletal system, which is still growing and therefore more easily damaged by using heavy weights.
Yes. Working out of course runs the gammut of cardio, weight lifting, running, etc. Good light to moderate weight training, reasonable cardio and aerobics, and even fairly intense sports are just fine, assuming there is regular medical well care. However, weight training, max lifting, and muscle building are best done once growth plates have closed. At 15, multiple reps with lower weights is better.
Depends ? workout. Workout is a generic term that can mean a variety of things. Regular exercise to an age appropriate standard is great for everyone. If as i suspect you mean weightlifting /body building or other such endevors, a lot depends on the kid. The aap advises such workouts be limited to those who have reached skelatal maturity & learned technique from a qualified trainer.Pediatrics 121(4)pp835-840, 2008.