SOURCE

new Vue({
  el: "#app",
  data: {
    background: '#ccc',
    width: 100,
    height: 100,
    contenteditable: true,
    width2:100
  },
  methods: {
    changeColor: function () {
      this.background="red"
    },
    change2:function(){
      this.width2="200",
        this.background="blue"
    }
  }
})

<div id="app">
  <div v-bind:style="{background:background,
  width:width+'px', 
  height:height+'px'}"  :contenteditable=contenteditable>
  </div>
  <button v-on:click="changeColor">change
  </button>
  <div v-bind:style="{background:background,
                    width:width2+'px',height:height+'px'}">
  </div>
  <button v-on:click="change2">change2</button>
</div>