If you know only one specific dimension, grab the corresponding green handle and hold Shift for keeping the other dimensions in proportion.
So:
- Select object
- Select Scale Tool
- Click on the right handle, move the mouse in a direction
- Hold Shift, then Click and let go of the mouse
- Type desired length. including units! (otherwise it uses scale factor) eg. 3" hit Enter
This way, you scale the bounding box of the object.