A building 50 ft high casts a 75-ft shadow. Sarah casts a 6-ft 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

anonymous · Answer

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anonymous · Answer

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.