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Australian AMC 2018 - Intermediate Question 24

AMC AUSTRALIA · Australian AMC 2018 - Intermediate

Question 24

In triangle $PQR$, $U$ is a point on $PR$, $S$ is a point on $PQ$, $T$ is a point on $QR$, with $US\parallel RQ$ and $UT\parallel PQ$.

The area of triangle $PSU$ is $120\text{ cm}^2$ and the area of triangle $TUR$ is $270\text{ cm}^2$.

The area of triangle $QST$, in square centimetres, is

Question illustration
  1. 150
  2. 160
  3. 170
  4. 180
  5. 200