ΔXYZ ∼ ΔGST and XY : GS = 2 : 3, XV is the median to the side YZ, and GD is the median to the side ST. The value of $(\frac{YV}{SD})^2$ is ______.

$\frac{4}{9}$

Given

⇒ ΔXYZ ∼ ΔGST and XY : GS = 2 : 3

⇒ \(\frac{XY}{GS}\) = \(\frac{XZ}{GT}\) = \(\frac{YV}{SD}\) = \(\frac{VZ}{DT}\)

⇒ \(\frac{XY}{GS}\) = \(\frac{YV}{SD}\)

⇒ \(\frac{2}{3}\) = (\(\frac{YV}{SD}\))²  

⇒ (\(\frac{YV}{SD}\))²  = \(\frac{4}{9}\)