In \(\displaystyle\triangle{S}{T}{R},\triangle{V}{W}{U}\):

\(\displaystyle\angle{S}\stackrel{\sim}{=}\angle{V}\)

\(\displaystyle\angle{T}\stackrel{\sim}{=}\angle{W}\)

By A-A similarity, the \(\displaystyle\triangle{S}{T}{R}\sim\triangle{V}{W}{U}\).

SP=PR=x

\(\displaystyle\Rightarrow{S}{R}={2}{x}\)

UQ=QV=3

\(\displaystyle\Rightarrow{U}{V}={6}\)

In two similar triangles, the ratio of their corresponding sides, medians are equal.

\(\displaystyle{\frac{{{S}{R}}}{{{V}{U}}}}={\frac{{{T}{P}}}{{{W}{Q}}}}\)

\(\displaystyle\Rightarrow{\frac{{{2}{x}}}{{{6}}}}={\frac{{{13.5}}}{{{9}}}}\)

\(\displaystyle\Rightarrow{x}={4.5}\)

\(\displaystyle\angle{S}\stackrel{\sim}{=}\angle{V}\)

\(\displaystyle\angle{T}\stackrel{\sim}{=}\angle{W}\)

By A-A similarity, the \(\displaystyle\triangle{S}{T}{R}\sim\triangle{V}{W}{U}\).

SP=PR=x

\(\displaystyle\Rightarrow{S}{R}={2}{x}\)

UQ=QV=3

\(\displaystyle\Rightarrow{U}{V}={6}\)

In two similar triangles, the ratio of their corresponding sides, medians are equal.

\(\displaystyle{\frac{{{S}{R}}}{{{V}{U}}}}={\frac{{{T}{P}}}{{{W}{Q}}}}\)

\(\displaystyle\Rightarrow{\frac{{{2}{x}}}{{{6}}}}={\frac{{{13.5}}}{{{9}}}}\)

\(\displaystyle\Rightarrow{x}={4.5}\)