Here's one way but not sure if it's the best or the easiest. Goto the "Create" menu and select "Measure Tools" and then "Distance Tool". Then click on one side of the mesh and then the other side of the mesh. You now know the distance. Then group the two points you just clicked and the mesh together. Now when you scale your mesh, the measurement will change with it and give you instantaneous measurements. You'll just have to make sure that the measurements are aligned with the direction of your scale.

I have Maya 8.5 so if your version is older, the measure tools might be somewhere else. Hope this helps you out a little.