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SMO 2006 Senior Round 1 Question 28

SMO · SMO 2006 Senior Round 1

Question 28

In the figure below, $S$ is on $QR$ and $U$ is on $PR$. Segments $PS$ and $QU$ intersect at $T$. It is given that $PT=TS$ and $QS=2RS$. If the area of $\triangle PQR$ is $150$ cm$^2$ and the area of $\triangle PSU$ is $x$ cm$^2$, find $x$.

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