I had a requirement to host the content of one responsive web application inside a view of another responsive web application. Since both applications were responsive in design there was no definitive height, width or aspect ratio. I found a tutorial here: https://benmarshall.me/responsive-iframes/ which talks about a library called Pym.js and also has some css/js examples of a simpler approach. I decided that using Pym.js was overkill for my needs, mostly because I didn't want to make any code changes to the target site. The code I found on the above link also didn't quite work for my needs, since I didn't have a particular aspect ratio (it will depend on the viewing device) and also couldn't give a hard-coded initial width/height to the iframe. In my case, the aspect ratio is actually dependant on the viewing devices screen, therefore I changed the script slightly as below:
$(document).ready(function () {
            var $responsive_iframes = $(".responsive_iframe");

            // Resize the iframes when the window is resized
            $(window).resize(function () {
                $responsive_iframes.each(function () {
                    // Get the parent containe's width and the screen ratio
                    var width = $(this).parent().width();
                    var ratio = $(window).height() / $(window).width();

                    $(this).width(width)
                          .height(width * ratio);
                });
                // Resize to fix all iframes on page load.
            }).resize();
        });
(I also made the jQuery selector look for a class name, rather than all iframes)