A street lamp casts a shadow 31.5 feet long, while an 8 foot-tall street sign casts a shadow of 14 feet long. What is the length and height of the lamp?

The answer to your question is the height of the lamp is 18.2 ft

Step-by-step explanation:

Data

Street lamp shadow = 31.5 ft

Street sign height = 8 ft

Street sign shadow = 14 ft

Street lamp height = x

Process

1. - To find the height of the lamp use proportions. In this kind of problem, we do not look for the length, but the shadow.

Street lamp height/street lamp shadow = street sign height/street sign

shadow

Substitution

x / 31.5 = 8 / 14

Solve for x

x = (31.5) (8) / 14

Simplification

x = 254.4 / 14

Result

x = 18.2 ft