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Australian AMC 2013 - Senior Question 29

AMC AUSTRALIA · Australian AMC 2013 - Senior

Question 29

The points X, Y and Z are on the sides of $\triangle PQR$ as shown, such that

$$QZ:ZY:YR=1:2:3\quad\text{and}\quad PX:XR=4:5.$$

Question illustration

If $QS=11$ cm, find the length of ST, in centimetres.