Question

Which value of TR would make ST parallel to QR?

Answer 1

We have to find the value of TR that will make ST || QR.

For ST to be parallel to QR, then we have to make triangles PST and PQR become similar.

Similar triangles will have corresponding sides that are proportional.

Then, we could write proportions between the sides as:

`(PS)/(PQ)=(PT)/(PR)`

Then, we can replace with the information we have and solve for TR as:

`\begin{gathered} (PS)/(PQ)=(PT)/(PR) \\ (PS)/(PS+SQ)=(PT)/(PT+TR) \\ (6)/(6+18)=(4)/(4+TR) \\ 6(4+TR)=4(6+18) \\ 6(4+TR)=4\cdot24 \\ 4+TR=(4\cdot24)/(6) \\ 4+TR=16 \\ TR=16-4 \\ TR=12 \end{gathered}`

Answer: TR = 12