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Marvin's son is 3ft tall. He casts a shadow of 1 foot. Marvin casts a shadow of 2.5ft. How tall is Marvin?

User FeelGood
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1 Answer

5 votes

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.

User Arxpoetica
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