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

Jason

6 June, 11:41

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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Riley Crane · 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.