Assuming that you are using the default master page, the size of the quick launch menu is fixed 150X400 pixels. If the content is anything more than this size it automatically adds scroll bars. To change size of this area open the default.master in SharePoint designer. Go to the code view and find SharePoint:SPRememberScroll tag. The style attribute has the size of the quick launch area.

Here is the default value

Style="overflow: auto;height: 400px;width: 150px; "

Simply change it to anything you like:

Style="overflow: auto;height: 400px;width: 250px; "

Cheers
Alireza