When you measure LxWxH, the number should add up to no more than 45" as per AA policy. There's definitely "wiggle room" on this though because some luggage pockets can be squooshed in. At many airports (usually at the gate), there's a little sample size box to put your carry on in to see if it would fit.
If it's within that kind of range though I highly doubt they will force you to check it