jQUERY: div same height as width 100% parent change dinamically

gistfile1.js

//html
<div class="home-item" style="background-image:url(http://placehold.it/500x500)"></div>
//css
.home-item {
    width:20%;
    background-position: center center;
    background-repeat: no-repeat;
    background-size: cover;
    float: left;
}

<script>
    $(window).load(function () {
        var divWidth = $('.home-item').width();
        $('.home-item').css({
            'height': divWidth + 'px'
        });
    });
    $(window).resize(function () {
        var divWidth = $('.home-item').width();
        $('.home-item').css({
            'height': divWidth + 'px'
        });
    });
</script>