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2017 AMC 10B Question 19

AMC10 · 2017 AMC 10B

Question 19

Let $ABC$ be an equilateral triangle. Extend side $\overline{AB}$ beyond $B$ to a point $B'$ so that $BB'=3 \cdot AB.$ Similarly, extend side $\overline{BC}$ beyond $C$ to a point $C'$ so that $CC'=3 \cdot BC,$ and extend side $\overline{CA}$ beyond $A$ to a point $A'$ so that $AA'=3 \cdot CA.$

What is the ratio of the area of $\triangle A'B'C'$ to the area of $\triangle ABC?$
  1. $9:1 $
  2. $16:1 $
  3. $25:1 $
  4. $36:1 $
  5. $37:1 $