Triangle $$ABC$$ is similar to triangle $$PQR$$ and $$AB : PQ = 2 : 3. AD$$ is the median to the side $$BC$$ in triangle $$ABC$$ and $$PS$$ is the median to the side $$QR$$ in triangle $$PQR.$$ What is the value of $$(\frac{BD}{QS})^2$$?
In the case of similar triangles AB/PQ =AC/PR =BC/QR
AB/PQ=2/3
AB/PQ=BC/QR
AB/PQ=2BD/2QS
AB/PQ=BD/QS
BD/QS=2/3
$$(\frac{BD}{QS})^2$$=4/9
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