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Australian AMC 2013 - Senior Question 19

AMC AUSTRALIA · Australian AMC 2013 - Senior

Question 19

A running track encloses an area formed by a rectangle joined to two semicircles, as shown in the diagram below. If the length of the track must be 400 metres, then what is the maximum possible area of the rectangle, in square metres?

Question illustration
  1. $\frac{160\,000}{(\pi+2)^2}$
  2. $\frac{20\,000}{\pi}$
  3. $\frac{30\,000}{\pi}$
  4. 10 000
  5. $\frac{40\,000}{\pi}$