Hola no se si lo que quieres es esto : lo he echo sin Jquery , con javascript
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1" />
<title>3dAtelier</title>
<head>
<!-- <script src="jquery-latest.
js"></script> -->
<script type="text/javascript">
function calcular_altura() {
if (document.body && document.body.offsetWidth) {
winW = document.body.offsetWidth;
winH = document.body.offsetHeight;
}
if (document.compatMode=='CSS1Compat' && document.documentElement && document.documentElement.offsetWidth ) {
winW = document.documentElement.offsetWidth;
winH = document.documentElement.offsetHeight;
}
if (window.innerWidth && window.innerHeight) {
winW = window.innerWidth;
winH = window.innerHeight;
}
return winH;
}
function cambiar_logo () {
var alto= calcular_altura();
var ancho = parseFloat(alto)*4.35;
ancho=parseInt(ancho);
document.getElementById("imagen_logo").width=ancho ;
document.getElementById("imagen_logo").height=alto ;
}
</script>
</head>
<body onresize="cambiar_logo()" onload="cambiar_logo()">
<img id="imagen_logo" src="images/logo.jpg" width="100px" height="25px" alt="Logo" />
</body>
</html>