Australian AMC 2017 - Senior Question 14

Question 14

In the triangle shown, $PQ=SQ=SR=QR$ and $\angle STR=90^\circ$. The points $P,Q,T,R$ lie on one straight line in that order. The ratio $TR:PS$ is equal to

Question illustration

$1:\sqrt3$
$1:2\sqrt3$
$1:2$
$1:\sqrt2$
$1:\frac{3\sqrt3}{2}$