Question

A 1.5 m tall boy stands at a distance of 2m from lamp post and cast a shadow of 4.5m on the ground. Find the height of lamp post.​

Answer 1

Solution:-

Given:-

=> Height of boy = 1.5 m

=> Standing at a distance of 2 m from lamp post

=> its form a shadow 4.5 m

So

∆ABE & ∆CDE are similar its form same shape

$\to \rm \: \dfrac{DE}{AD + DE} = \dfrac{CD}{AB}$

$\to \rm \: value \: \\ \rm \: DE = 4.5 \\ \: \rm AD = 2 \\ \: \rm \: CD = 1.5 \\ \rm \: AB = h$

Put the value

$\to \rm \: \dfrac{4.5}{2+ 4.5} = \dfrac{1.5}{h}$

$\to \rm \: \dfrac{4.5}{6.5} = \dfrac{1.5}{h}$

$\to \rm \: \dfrac{45}{65} = \dfrac{15}{10h}$

$\to \rm \: \dfrac{ {}^{3} \cancel{45}}{65} = \dfrac{ \cancel{15}}{10h}$

$\to \rm \: \dfrac{3}{65} = \dfrac{1}{10h}$

$\rm \to \: 30h = 65$

$\rm \to \: h = \dfrac{65}{30}$

$\rm \to \: h = 2.16m$

height of lamp post is 2.16 m

Answer 2

Answer:

2.16 m

Step-by-step explanation:

both the triangles are similar

so,  1.5/4.5 = h/ 2+4.5

1/3=h/6.5

h=6.5/3

=2.16m