Can some please tell me how can i apply CSS height in % for inner div?

what i am trying to do is applying a bg color to an inner div ( fill class div ) based on height in %

Below is the code, this works just fine when i remove the doctype

How can make it work with XHTML 1.0 Transitional DOCTYPE

Code:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
...