If both parents of an adolescent child get sentenced to prison for 10 years, what happens to the child?

If there's no relative to take them in they'd go into foster care.

The kid will be placed with family or a friend and if that's not available the kid will be put in Foster care as a ward of the state.

Goes into foster care or goes to some relative.

Maybe the child can run away from home and join the circus! Anything is better than living with strangers or relatives who don't want you.

If there was a family member willing to take them in then that would be the answer.

If not they would become a ward of court and be placed in foster care then once 16 (in UK) they are free to choose where they live.

Technically, they become wards of the state. If a family member was available to take custody, they would likely be placed with them. Otherwise, they would enter the foster care system until the parents were released.

Why they go to the prison with the parents.

YOU don''t want to separate a child from its parents JUST because they broke the law do you?

They either find a suitable family member to raise the child or foster care

It goes into the foster care system if there are not suitable arrangements for immediate or extended family to take on the responsibility of adoption.