Percentage Height HTML 5/CSS

I am trying to set a <div> to a certain percentage height in CSS, but it just remains the same size as the content inside it. When I remove the HTML 5 <!DOCTYTPE html> however, it works, the <div> taking up the whole page as desired. I want the page to validate, so what should I do?

I have this CSS on the <div>, which has an ID of page:

#page {
    padding: 10px;
    background-color: white;
    height: 90% !important;
}