7 Cassie wants to determine the length of the shadow that a 20-foot tall telephone pole casts without measuring it. If Cassie's mailbox, which is 45 inches in height, casts a shadow that is 22.5 inches in length, how long is the shadow that the telephone pole casts?
Accepted Solution
A:
Answer:10 ftStep-by-step explanation:In order to solve this question, we need to set up a proportion:[tex]\frac{\textrm{Height of mailbox}}{\textrm{Length of shadow}} = \frac{\textrm{Height of telephone pole}}{\textrm{Length of shadow}}[/tex]Replacing with actual values:[tex]\frac{45 \textrm{ in}}{22.5 \textrm{ in}} = \frac{20 \textrm{ ft}}{x \textrm{ ft}}[/tex]Cross-multiplying:[tex]45\times{x} = 20\times{22.5}\\45x = 450[/tex]Dividing both sides by 45:[tex]\frac{45x}{45} = \frac{450}{45}\\\\x = 10[/tex]Therefore, the length of the telephone pole's shadow is 10 ft.