It is the length of the bag you are carrying.
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Linear inch is a phantasy word from the airliners. It means: X linear inches = length + width + depth (measured in inches). Inches are still inches. "Linear" inches are not made up. Inches refers to the measurement along a line as opposed to square inches (for area) and cubic inches (for volume).
What do you mean? 40 inches = 40 inches.
do you mean 28 inches by 9 inches by 18 inches? That is 28+9+18 = 55 linear inches by airplane luggage standards
If you mean perimeter length of a 30 inch diameter circle, then it is 30*Pi or 94.248 inches (rounded to 3rd decimal).
Linear means a straight line.