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Australian AMC 2012 - Senior Question 10

AMC AUSTRALIA · Australian AMC 2012 - Senior

Question 10

The architecture of Federation Square in Melbourne is based on frames as shown in which a large triangle is subdivided into 5 identical triangles, each similar to the large triangle.

Question illustration

If the shortest side of one of the smallest triangles is 1 m, how many metres of framing are required to construct the whole shape?
  1. 20
  2. $8+4\sqrt5$
  3. $10+4\sqrt5$
  4. $12+4\sqrt5$
  5. $15+5\sqrt5$