Scale element proportional to Background Cover with jQuery

I have a tricky question: I have a fullsize background over the site I'm working on. Now I want to attach a div to a certain position on the image and also that the div scales in the same way the my background image with the "background-size: cover" property does. So in this example, I have a picture of a city, which covers the browser window and I want my div to overlay one particular building, no matter of the window size.

I already managed to make the div sticking to one position, but cant make it resize properly. What I did so far:

http://codepen.io/EmmieBln/pen/YqWaYZ

var imageWidth = 1920,
    imageHeight = 1368,
    imageAspectRatio = imageWidth / imageHeight,
    $window = $(window);

var hotSpots = [{
    'x': -160,
    'y': -20,
    'height': 400,
    'width': 300
}];

function appendHotSpots() {
    for (var i = 0; i < hotSpots.length; i++) {
        var $hotSpot = $('<div>').addClass('hot-spot');
        $('.container').append($hotSpot);
    }
    positionHotSpots();
}

function positionHotSpots() {
    var windowWidth = $window.width(),
        windowHeight = $window.height(),
        windowAspectRatio = windowWidth / windowHeight,
        $hotSpot = $('.hot-spot');

    $hotSpot.each(function(index) {
        var xPos = hotSpots[index]['x'],
            yPos = hotSpots[index]['y'],
            xSize = hotSpots[index]['width'],
            ySize = hotSpots[index]['height'],
            desiredLeft = 0,
            desiredTop = 0;

        if (windowAspectRatio > imageAspectRatio) {
            yPos = (yPos / imageHeight) * 100;
            xPos = (xPos / imageWidth) * 100;
            xSize = (xSize / imageWidth) * 1000;
            ySize = (ySize / imageHeight) * 1000;
        } else {
            yPos = ((yPos / (windowAspectRatio / imageAspectRatio)) / imageHeight) * 100;
            xPos = ((xPos / (windowAspectRatio / imageAspectRatio)) / imageWidth) * 100;
        }

        $(this).css({
            'margin-top': yPos + '%',
            'margin-left': xPos + '%',
            'width': xSize + 'px',
            'height': ySize + 'px'
        });

    });
}

appendHotSpots();
$(window).resize(positionHotSpots);

My idea was: If (imageWidth / windowWidth) < 1 then set Value for var Scale = (windowWidth / imageWidth) else var Scale ( windowHeight / imageHeight ) and to use the var Scale for transform: scale (Scale,Scale) but I couldnt manage to make this work…

Maybe you guys could help me out…