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MathNet 2004 — Part 02 Question 56

Math Olympiad Vault · MathNet 2004 — Part 02

Question 56

Let $B$ be a point inside the segment $AC$ with $AB$ of length $2$ and $BC$ of length $3$. Having constructed the equilateral triangles $ABA'$ and $CBC'$, on the same side with respect to the segment $AC$, how much does the area of ​​the triangle $A'BC'$ measure?
  1. $\frac{3}{2} \sqrt{3}$
  2. $3$
  3. $3 \sqrt{3}$
  4. $5$
  5. $\frac{25}{8} \sqrt{3}$.