Question

a boy 165 cm tall casts a shadow of 110 cm. the lamp post casts a shadow of 405 cm. how high is the lamp post?

○ x = 607.5 cm

○ x = 420 cm

○ x = 750 cm

○ x = 1005 cm

Explanation:

Step1: Set up proportion

Let \( x \) be the height of the lamp post. The ratio of height to shadow length should be equal for the boy and the lamp post. So, \(\frac{165}{110}=\frac{x}{405}\).

Step2: Solve for \( x \)

Cross - multiply: \(110x = 165\times405\).
First, calculate \(165\times405 = 165\times(400 + 5)=165\times400+165\times5 = 66000+825 = 66825\).
Then, \(x=\frac{66825}{110}=607.5\).

Answer:

\( x = 607.5\) cm (the option: \( x = 607.5\) cm)