In the above figure, let PD be the girl, AB be the lamp post. Given that, the girl stands at a distance of 3 m from the lamp post. So BP = 3 m. Also the height of the girl is 1.5 m. So PD = 1.5 m. The shadow of the girl cast is of the length 4.5 m. So PC = 4.5 m. Then we have to find the height of the lamp post, that is, AB.

Now, BC = BP + PC = 3 + 3.5 = 7.5 m.

From ∆DPC,

∠ACB = ∠DCP. So,

From, ∆ABC,

or,

or,

Hence the correct choice is C.