Q12 of 58 Page 665

If a 1.5-m-tall girl stands at a distance of 3 m from a lamp post and casts a shadow of length 4.5 m on the ground, then the height of the lamp post is

Untitled35.jpg


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.

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