Question

A 150cm tall boy stands at a distance of 8cm from a lamp post and casts a shadow of 2m find the height of lamp post.

Answer 1

Let BC=X. AD=150 CM .150/100=1.5m. BD=8m DE=2m. BC/AD=BD/DE. (thales theorem) X/1.5 =8/2 2x=8×1.5  2x=12. X=12/2.   X= 6. Height of the lamp post is 6m

Answer 2

Convert all to cm:

2m = 200 cm

Define x:

Let the height of the lamp post be x

Using the property of similar triangle:

$\dfrac{\text{height 1}}{\text{height 2}} = \dfrac{\text{Distance 1}}{\text{Distance 2}}$

Sub the known values into the equation:

$\dfrac{\text{150}}{\text{x}} = \dfrac{\text{200}}{\text{208}}$

Cross multiply:

$200x = 208 \times 150$

Combine like terms:

$200x = 31200$

Divide both sides by 200:

$x = 156$

Answer: The height of the lamp post is 156 cm