# Difference between revisions of "2017 AMC 12B Problems/Problem 15"

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## Revision as of 18:15, 16 February 2017

## Problem 15

Let be an equilateral triangle. Extend side beyond to a point so that . Similarly, extend side beyond to a point so that , and extend side beyond to a point so that . What is the ratio of the area of to the area of ?

## Solution

Solution by HydroQuantum

Let .

Recall The Law of Cosines. Letting , . This simplifies to . Since both and are both equilateral triangles, they must be similar due to similarity. This means that .

Therefore, our answer is .