Example 7
A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
Given: Lamp post (AB) = 3.6m
Height of girl (CD)=90 cm = 90/100 m = 0.9 m
Speed = 1.2 m/sec.
To Find : Length of her shadow i.e. DE
Solution: -
The girl walks BD distance in 4 seconds
We know that,
Speed = /( )
Speed = /( )
1.2 = /4
1.2 4=
4.8 =
BD = 4.8 m
Now , in
E = E
B = D
Therefore, using AA Similarity criterion
So, ~
We know that if two triangles are similar,
their sides are in proportion
/ = /
( + )/ = /
(4.8 + )/ =3.6/0.9
(4.8 + )/ =36/9 10/10
(4.8 + )/ =4
4.8 + DE = 4 DE
4.8 = 4DE DE
4.8 = 3DE
3DE = 4.8
DE = 4.8/3
DE = 48/(3 10)
DE = 16/10 = 1.6 m
Hence , shadow is 1.6 m long

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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