JSFiddle - React, Tailwind, and code Playground

HTML

<select id="resizing_select">
 <option>All</option>
 <option>Longer</option>
 <option>A very very long string...</option>
</select>
<select id="width_tmp_select">
 <option id="width_tmp_option"></option>
</select>

CSS

#resizing_select {
 width: 50px;
} 
 
#width_tmp_select{
 display : none;
}

JavaScript

$(document).ready(function() {
 $('#resizing_select').change(function(){
    $("#width_tmp_option").html($('#resizing_select option:selected').text());
    $(this).width($("#width_tmp_select").width());  
 });
});