ΔABC is similar to ΔPQR and AB : PQ = 2 : 3. AD is the median to the side BC in ΔABC and PS is the median to the side QR in ΔPQR. What is the value of (BD/QS) 2?
4/9
Since \(\triangle ABC\sim\triangle PQR\), corresponding sides share the ratio \(\dfrac{AB}{PQ}=\dfrac{BC}{QR}=\dfrac{2}{3}\).
AD and PS are medians, so D and S are midpoints, giving \(BD=\tfrac{1}{2}BC\) and \(QS=\tfrac{1}{2}QR\). Therefore:
\[\frac{BD}{QS}=\frac{BC}{QR}=\frac{2}{3}\]
\[\left(\frac{BD}{QS}\right)^2=\left(\frac{2}{3}\right)^2=\frac{4}{9}\]
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