Question

7. If APTS-APQR, find the value of x. Show your work.5x + 13Р36306x-2SR

Answer 1

Given, ΔPTS~ΔPQR.

The ratio of corresponding sides of similar triangles are equal. Hence,

`(PQ)/(PT)=(QR)/(TS)`
`\begin{gathered} (5x+13)/(36)=(6x-2)/(30) \\ (5x+13)/(6)=(6x-2)/(5) \\ (5x+13)5=(6x-2)6 \\ 5*5x+13*5=6x*6-2*6 \\ 25x+65=36x-12 \\ 65+12=36x-25x \\ 77=11x \\ (77)/(11)=x \\ 7=x \end{gathered}`

Therefore, the value of x is 7.