Edit in JSFiddle

<div class="container">
    <div class="outer r4x3">
        <div class="inner">
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
        </div>
    </div>
</div>

<div class="container">
    <div class="outer r2x1">
        <div class="inner">
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
            <div class="little-box">A</div>
            <div class="little-box">B</div>
            <div class="little-box">C</div>
            <div class="little-box">D</div>
        </div>
    </div>
</div>

/* container defines margins and width */
.container {
    margin: 60px 120px 0;
}

/* outer container will define aspect ratio */
.outer {
    position: relative;
    width: 100%;
}

.outer.r4x3 {
    padding-top: 75%; /* "height" will be 3/4 of width */
}

.outer.r2x1 {
    padding-top: 50%; /* "height" will be 1/2 of width */
}

/* inner container positioned absolutely and holds content */
.outer .inner {
    position: absolute;
    top: 0;
    left: 0;
    right: 0;
    bottom: 0;
    outline: 1px solid grey;
}

/* example content */
.little-box {
    float: left;
    outline: 1px solid steelblue;
    width: 25%;
    height: 33.333%;
}

/* just for display purposes... */
.inner::after {
    content: attr(data-size);
    position: absolute;
    left:0;
    top: -1em;
}

// this javascript is simply to display the size of the box
// you'll see some rounding errors from the percentage calculation in CSS

$(window).on('resize', function(){

    $('.inner').each(function(){

        var box = $(this);        
        var width = box.width();
        var height = box.height();        
        
        box.attr('data-size', width+'x'+height+' (r: '+(width/height).toFixed(2)+')');

    });
}).trigger('resize');