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

Hydroquantum (talk | contribs) (→Solution) |
Hydroquantum (talk | contribs) (→Solution) |
||

Line 8: | Line 8: | ||

Solution by HydroQuantum | Solution by HydroQuantum | ||

− | Let <math>AB=BC=CA=x | + | Let <math>AB=BC=CA=x</math>. |

## Revision as of 17:15, 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 .