A building 50 ft casts a 75 ft shadow. Sarah casts a 6ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?

Question

Mathematics

Yael Lawrence

10 November, 11:15

A building 50 ft casts a 75 ft shadow. Sarah casts a 6ft shadow. The triangle formed by the building and its shadow is similar to the triangle formed by Sarah and her shadow. How tall is Sarah?

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Adriel Yoder · Answer 1

Since the triangles are similar, the side lengths are proportional. In other words, if a 50 foot building makes a 75 foot shadow, that is a ratio of 50/75, or 2/3 if you reduce it. This is the same ratio that describes Sarah's height, S, compared to her shadow, which the problem says is 6 feet long. So 2/3 = S / 6 You can cross multiply to find S ... 12 = 3S ... so S = 4 feet tall ... Sarah is 4 feet tall.