Edit in JSFiddle

<div class="header">
    <ul>
        <li><a href="#auto">Auto</a></li>
        <li><a href="#fit">Fit</a></li>
        <li><a href="#wide">Wide</a></li>
    </ul>
</div>
<div class="container box">
    
    <div class="anchor" id="auto"></div>
    <div class="section red">
        <p>Auto height and width</p>
    </div>
    <div class="section green">
        <p>Auto height and width</p>
        <p><img src="http://placehold.it/640x360" alt="" /></p>
    </div>
    <div class="section blue">
        <p>Auto height and width</p>
    </div>
    <div class="section yellow">
        <p>Auto height and width</p>
    </div>
    
    <div class="anchor" id="fit"></div>
    <div class="section fit red">
        <div class="t">
            <div class="tc">
                 <h1>Fit</h1>
                <p>width and height</p>
            </div>
        </div>
    </div>
    <div class="section fit green">
        <div class="t">
            <div class="tc">
                 <h1>Fit</h1>
                <p>width and height</p>
            </div>
        </div>
    </div>
    <div class="section fit blue">
        <div class="t">
            <div class="tc">
                 <h1>Fit</h1>
                <p>width and height</p>
            </div>
        </div>
    </div>
    <div class="section fit yellow">
        <div class="t">
            <div class="tc">
                 <h1>Fit</h1>
                <p>width and height</p>
            </div>
        </div>
    </div>

    <div class="anchor" id="wide"></div>
    <div class="section wide red">
        <div class="content">
            <div class="t">
                <div class="tc">
                     <h1>Widescreen</h1>
                    <p>16:9</p>
                </div>
            </div>
        </div>
    </div>
    <div class="section wide green">
        <div class="content">
            <div class="t">
                <div class="tc">
                     <h1>Widescreen</h1>
                    <p>16:9</p>
                </div>
            </div>
        </div>
    </div>
    <div class="section wide blue">
        <div class="content">
            <div class="t">
                <div class="tc">
                     <h1>Widescreen</h1>
                    <p>16:9</p>
                </div>
            </div>
        </div>
    </div>
    <div class="section wide yellow">
        <div class="content">
            <div class="t">
                <div class="tc">
                     <h1>Widescreen</h1>
                    <p>16:9</p>
                </div>
            </div>
        </div>
    </div>
</div>

/* important style */

html, body {
    margin: 0;
    height: 100%;
}

.header {
    width: 100%;
    z-index: 2;
    position: fixed;
    background-color: #666;
}

.header ul {
    margin: 0;
    padding: 0;
    overflow: auto;
    list-style: none;
}

.header li {
    float: left;
    padding: 10px;
}

.header li a {
    color: #fff;
}

.container {
    padding-top: 38px;
    /* offset the height of the fixed nav to ensure height 100% is correct */
    height: 100%;
}

.box {
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
    box-sizing: border-box;
}

.section {
    position: relative;
    width: 100%;
}

.section img {
    max-width: 100%;
}

.anchor {
    padding-top: 38px;
    margin-top: -38px;
}

.section p {
    margin: 0;
}

/* sizes */

.fit {
    height: 100%;
}

.wide {
    height: auto;
    padding-top: 56.25%;
    /* 9 / 16 = 0.5625 */
}

.wide .content {
    position: absolute;
    top: 0;
    left: 0;
    bottom: 0;
    right: 0;
}

/* centering */

.t {
    display: table;
    width: 100%;
    height: 100%;
}

.tc {
    display: table-cell;
    vertical-align: middle;
    text-align: center;
}

/* colours */

.red {
    background-color: red;
}
.green {
    background-color: green;
}
.blue {
    background-color: blue;
}
.yellow {
    background-color: yellow;
}