Question 390901
There are two lamp posts (A and B) both 9.6m tall.
When a man 1.6m tall stand X meters in front of lamp post A, his shadow casted
 by lampost B just touches the base of lampost A.
The man then walks towards lamp post B for 12m and his shadow, casted by lamp
 post A, just touches the base of Lamp post B.
What is the length of the man's shadow.
:
We can use the rule of similar right triangles here
The sides of the large triangle formed by the light pole (9.6) and the dist
between the poles, (2x+12)
:
The sides of the small triangle formed by the man (1.6) and the dist from
him to the light pole, x
:
A ratio equation
{{{9.6/1.6}}} = {{{(2x+12)/x}}}
Cross multiply
9.6x = 1.6(2x+12)
9.6x = 3.2x + 19.2
9.6x - 3.2x = 19.2
6.4x = 19.2
x = {{{19.2/6.4}}}
x = 3 meters is the guys shadow