Answer:
the height of the lamppost is 2.7 meters.
Step-by-step explanation:
Proportion states that two ratios or fractions are equal.
As per the statement:
A boy who is 1.8 meters tall stands 1 meter away from a lamppost and casts a shadow 2 meters long.
You can see the diagram as shown below.
by definition of proportion we have;
[tex]\frac{\text{height of the boy}}{\text{Shadow of boy}}=\frac{\text{height of the lamppost}}{\text{Shadow of lamppost}}[/tex]
From the diagram:
height of the boy = 1.8 meter tall , shadow of the boy = 2 meter long, height of the lamppost = h meter and shadow of the lamppost = 1+2 = 3 meter
[tex]\frac{1.8}{2}= \frac{h}{3}[/tex]
⇒[tex]0.9 = \frac{h}{3}[/tex]
Multiply both sides by 3 we have;
2.7 = h
or
h = 2.7 meter
Therefore, the height of the lamppost is 2.7 meters.
