Final answer:
By setting up a proportion based on similar triangles formed by the shadows and heights of Marvin and his son, we find that Marvin is 7.5 feet tall.
Step-by-step explanation:
The question involves solving a problem using the concept of similar triangles. Since Marvin's son is 3 feet tall and casts a 1-foot shadow, and Marvin casts a 2.5-foot shadow, we can set up a proportion to find Marvin's height. The ratio of height to shadow length for Marvin's son is 3 to 1, which should be the same for Marvin because they are formed under the same conditions.
Let h represent Marvin's height. Thus, the proportion is:
3 ft / 1 ft = h / 2.5 ft
Cross-multiply to find the value of h:
3 ft × 2.5 ft = 1 ft × h
7.5 = h
Therefore, Marvin is 7.5 feet tall.