<div id="Div2">Hello2</div>
<br>
<div id="Div1">Hello1</div>

#Div1{
    background-color:blue;
}

#Div2{
    background-color:red;
}

$(document).ready(function(){
    document.onchange=setDivHeight();

function setDivHeight(){
    var x=Number(document.getElementById('Div1').style.height)
    document.getElementById('Div2').style.height=x;
}

});



setInterval(function() {
   $('#Div1').eq(0).append('<p>appended content</p>')
}, 1000)

div{
    vertical-align: top;
}