The triangles PTS and POR are similar, so we can take the ratios of the side to order
[tex]\frac{PT}{ST}=\frac{PQ}{SQ}[/tex]
[tex]\frac{36}{30}\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}[/tex]
[tex]\begin{gathered} \text{cross multiplying} \\ \\ 30\text{ (6x - 2) = 30 (5x + 13)} \\ \\ \text{Expanding the parenthesis} \\ \\ 30\text{ x 6x - 30 x 2 = 30 x 5x + 30 x 13} \\ \\ 180x\text{ -60 = 150x + 390} \end{gathered}[/tex]
We can then solve for x by collecting like terms
180x - 150x = 390 + 60
30x = 450
Divide both sides by 30
x = 450/ 30
x = 15
