Final answer:
Using similar triangles and the given proportions, we calculate the height of the lamp post, which results in 800 cm, though this option is not provided among the given answers.
Step-by-step explanation:
To find the height of the lamp post given the information about the girl's shadow and height, we use similar triangles. In similar triangles, the ratios of corresponding sides are equal. Therefore, we can set up a proportion using the girl's height and shadow length and the unknown lamp post height and its distance from the girl's shadow. The proportion is as follows:
Girl's height / Girl's shadow length = Lamp post height / Lamp post's distance from the girl
160 cm / 90 cm = Lamp post height / (360 cm + 90 cm).
Solving for the lamp post height:
Lamp post height = (160 cm / 90 cm) × (360 cm + 90 cm)
Lamp post height = (160 cm / 90 cm) × 450 cm
Lamp post height = 800 cm.
However, among the given options, there is no 800 cm. This indicates that there must be an error in the options provided, as they do not include the correct answer based on the calculation.