Question

1. using ratios an entrepreneur wants to rent a billboard at least 30 feet tall to display an advertisement for her business. she is 5 feet 6 inches tall and casts a shadow 7 feet long. at the same time, a billboard casts a shadow 35 feet long. is the billboard tall enough?

Explanation:

Step1: Convert height to feet

5 feet 6 inches is \( 5 + \frac{6}{12} = 5.5 \) feet.

Step2: Set up proportion

Let \( h \) be the billboard's height. The proportion is \( \frac{5.5}{7} = \frac{h}{35} \).

Step3: Solve for \( h \)

Cross - multiply: \( 7h = 5.5\times35 \). Then \( h=\frac{5.5\times35}{7} \). Calculate \( 5.5\times35 = 192.5 \), and \( \frac{192.5}{7}=27.5 \) feet.

Step4: Compare with 30 feet

27.5 feet is less than 30 feet.

Answer:

No, the billboard is not tall enough.