Given, ΔPTS~ΔPQR.
The ratio of corresponding sides of similar triangles are equal. Hence,
[tex]\frac{PQ}{PT}=\frac{QR}{TS}[/tex][tex]\begin{gathered} \frac{5x+13}{36}=\frac{6x-2}{30} \\ \frac{5x+13}{6}=\frac{6x-2}{5} \\ (5x+13)5=(6x-2)6 \\ 5\times5x+13\times5=6x\times6-2\times6 \\ 25x+65=36x-12 \\ 65+12=36x-25x \\ 77=11x \\ \frac{77}{11}=x \\ 7=x \end{gathered}[/tex]
Therefore, the value of x is 7.
