Question

a building casts a shadow that is 24 feet long. at the same time and nearby, a man that is 6 feet tall casts a shadow that is 2 feet long. image of building (red with a door, labeled height and 24 feet for shadow) and man (6 feet tall, shadow 2 feet long), with *not drawn to scale how tall is the building?
a. 28 feet
b. 36 feet
c. 48 feet
d. 72 feet
e. 96 feet

Explanation:

Step1: Set up proportion

Let \( h \) be the height of the building. The ratio of height to shadow length should be equal for the building and the man. So, \(\frac{h}{24}=\frac{6}{2}\)

Step2: Solve for \( h \)

Cross - multiply: \( 2h = 6\times24 \)
Calculate \( 6\times24 = 144 \), then \( 2h=144 \)
Divide both sides by 2: \( h=\frac{144}{2}=72 \)

Answer:

D. 72 feet