A single bond consists of a sigma electron could (orbital)....which in itself is the strongest type of bonding. But, when you create a double you are adding a pi orbital (which is weaker than sigma orbital), since the pi orbital is being added to an existing sigma orbital it logically follows that it will be a stronger one (pi and sigma > sigma), the effect of the pi orbital will be strengthening the overall bond (double bond) but also shortening the distance between the atoms,which means shorter bond. Triple bond on the other hand adds another pi orbital to the existing sigma and pi orbitals making the triple bond stronger than the previous two and also shorter.
Also note, that a double bond is not twice as strong as a single bond since we are not adding an additional sigma orbital, but a pi orbital (which is weaker), same logic extends to a triple bond.
Hope that helps.