One of the most important question from similarity chapter in which we have been asked to find how far a woman is away from the base of the pole using the properties of similarities, if a street light bulb is fixed on a pole 6 m above the level of street. If a woman of height casts a shadow of 3 m.
ML Aggarwal Avichal Publication class 10, chapter 13, question no 22
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 pole and woman be x m.
Here, woman and pole 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, ED/EB=CD/AB
⇒3/3+x=1.5/6
⇒3×6=1.5(3+x)
⇒18=4.5+1.5x
⇒1.5x=18−4.5=13.5
⇒x=13.5/1.5
=9m