Question

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?

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.