SolutioN :- Here we are provided with a diagram of a triangle. We need to find out the length of the segment LM . As we can see that , β KNL β MNL , [ By AAS ] Therefore , KN = MN ( by cpct ) β KN = MNβ 14x - 3 = 25 β 14x = 25 + 3β 14x = 28β x = 2 Put this x = 2 in LM :- β LM = 9x + 5 β LM = 9*2 + 5 β LM = 18 + 5 β LM = 23 Hence the required answer is 23 .