Silhouette Studio Basic Edition can not open SVG files, only DXF. The scaling of the design is lost when importing the DXF file. Adding a frame around the design matching the size it will be forced into when imported to Silhouette Studio will cause the scaling to be kept. For a quick way of doing this I created an extension with the option to add a frame matching the 8x12in or 12x12in cutting mat and media size in Silhouette Studio.
More details on how this works in the Link.