Dear Student,
Bond length are inversely proportional to percentage of s character.
With increase in s character bond length decrease. Hence we calculate the percentage s character in each compound.
Ethyne (H-C≡C-H): here carbon is sp hybridised : % s character = 50 %
Ethene (H2C=CH2): here carbon is sp2 hybridised : % s character = 33.3 %
Ethane (H3C-CH3): here carbon is sp3 hybridised : % s character = 25 %
As order % s character is ethane< ethene < ethyne, so the order of bond length is ethane > ethene > ethyne that is bond length is longest for ethane, smallest for ethyne and intermediate for ethene.
Regards,