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Australian AMC 2020 - Senior Question 20

AMC AUSTRALIA · Australian AMC 2020 - Senior

Question 20

Two sides of a regular pentagon are extended to create a triangle.
Inside this triangle, a smaller regular pentagon is drawn, as shown.
In area, how many times bigger is the larger pentagon than the smaller pentagon?

Question illustration
  1. 4
  2. $2\sqrt5$
  3. 5
  4. $\frac{\sqrt5+3}2$
  5. $\sqrt5$