Question

Andrew and Bob are standing next to each other outside. Andrew is 5.3 ft tall, and his shadow is 3.5 ft long. If Bob's shadow is 4 ft long, how tall is he?

a) 4.8 ft
b) 5.6 ft
c) 6.2 ft
d) 7.0 ft

Answer 1

By using the proportional relationship between the heights and shadow lengths of Andrew and Bob, we can determine that Bob's height is approximately 6 ft tall, although none of the provided answer choices are exact.

Step-by-step explanation:

The question involves solving a problem related to similar triangles, specifically using proportions to find the missing height of Bob given the information about Andrew's height and the length of their shadows. To solve the problem, we use the fact that the ratio of the height of a person to the length of their shadow is the same for both people since the Sun's rays are parallel.

For Andrew, we have the following ratio:

Height of Andrew / Length of Andrew's shadow = 5.3 ft / 3.5 ft.

For Bob, we have:

Height of Bob / Length of Bob's shadow = x / 4 ft, where x is Bob's unknown height.

To find the missing height of Bob, we set up a proportion:

5.3 ft / 3.5 ft = x / 4 ft.

Cross-multiplying gives us:

5.3 ft × 4 ft = x × 3.5 ft,

ownsolving for x gives:

x = (5.3 ft × 4 ft) / 3.5 ft.

x = 6.08 ft, which can be rounded to 6.1 ft, meaning that none of the provided options are correct. However, if we estimate x to 6.0 ft, Bob would be approximately 6 ft tall.