100% height div with xhtml

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If my page has a doc type tag of:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd";>

How do I create a div that sizes it's height to 100% of the page?

For example:
<div style="height:100%"></div> will not size to fit the page height, but
if I remove the DOCTYPE tag or set it to something other than XHTML the div
will resize.


.

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