Here is a live-cd image that contains the program parted. It is only around 50 Meg in size and contains many tools you could use to backup and change partitions on your hard drive.
It will resize a ext2, ext3 or reiserfs file system. However the start of the partition can't change. You could boot up with this disk ( your / and /var partitions won't be mounted then ) and back up the /var partition, delete /var, resize / , create a new /var, and restore /var.
Luckily, your /var partition is situated just after your / partition.