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MathNet 2014 Question 12

Math Olympiad Vault · MathNet 2014

Question 12

The segment $AB$ measures $20$ cm. The polygonal curve connecting the points $A$ and $B$ together with the segment $AB$ forms $7$ equilateral triangles. No segment of the polygonal curve lies on the segment $AB$. How long, in centimeters, is this polygonal curve?

Question illustration

(A) $40\sqrt{3}$

(B) $40$

(C) $20 + 20\sqrt{3}$

(D) $20 + 20\sqrt{2}$

(E) Impossible to determine.