Question

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?

Answer 1

Answer:

10 ft

Step-by-step explanation:

In order to solve this question, we need to set up a proportion:

$\frac{\textrm{Height of mailbox}}{\textrm{Length of shadow}} = \frac{\textrm{Height of telephone pole}}{\textrm{Length of shadow}}$

Replacing with actual values:

$\frac{45 \textrm{ in}}{22.5 \textrm{ in}} = \frac{20 \textrm{ ft}}{x \textrm{ ft}}$

Cross-multiplying:

$45\times{x} = 20\times{22.5}\\45x = 450$

Dividing both sides by 45:

$\frac{45x}{45} = \frac{450}{45}\\\\x = 10$

Therefore, the length of the telephone pole's shadow is 10 ft.