Question

8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R

Answer 1

The triangles PTS and POR are similar, so we can take the ratios of the side to order

`(PT)/(ST)=(PQ)/(SQ)`

`(36)/(30)\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}`

`\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}`

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