Take any rectangular prism. Let the lengths of the sides (width, height, and length) be $u,\,v,$ and $w.$ Then what is the surface area of this prism? It is just the sum of the areas of each face:
$S=2uv+2vw+2uw.$
If you increase each dimension by a factor of $x$, then the new dimensions are $ux,\,vx,$ and $wx.$ So what will the new surface area be? Now compare this to that of the original.