Question

A street lamp is fixed on pole of height 6 metres. A boy of height 1.5 meter cast the shadow of 3 meter. If the boy is standing in same line as lamp pole, then how far is the boy from the base of the lamp

Answer 1

Step-by-step explanation:

Let A be the position of the street bulb fixed on a pole AB=6 m and CD=1.5 m be the height of a woman and her shadow be ED=3 m.

Let distance between lamp and boy be x m.

Here, boy and lamp both are standing vertically.

So,CD∥AB

In △CDE and △ABE,∠E=∠E(common angle)

⇒∠ABE=∠CDE (each equal to 90° )

⇒∠BAE=∠ECD (Corresponding angles)

∴△CDE∼△ABE by AAA similarity criterion

Then,

EB AB

___ = ____

ED CD

⇒ 3 1.5

______ = ____

3+ x 6

⇒3×6=1.5(3+x)

⇒18=4.5+1.5x

⇒1.5x=18−4.5=13.5

⇒x= 1.5 =9m

___

13.5

⇒x = 9m