[jquery] jquery append div inside div with id and manipulate

Why not go even simpler with either one of these options:

$("#box").html('<div id="myid" style="display:block; float:left;width:'+width+'px; height:'+height+'px; margin-top:'+positionY+'px;margin-left:'+positionX+'px;border:1px dashed #CCCCCC;"></div>');

Or, if you want to append it to existing content:

$("#box").append('<div id="myid" style="display:block; float:left;width:'+width+'px; height:'+height+'px; margin-top:'+positionY+'px;margin-left:'+positionX+'px;border:1px dashed #CCCCCC;"></div>');

Note: I put the id="myid" right into the HTML string rather than using separate code to set it.

Both the .html() and .append() jQuery methods can take a string of HTML so there's no need to use a separate step for creating the objects.