Question

R1.56P12TSIn the diagram, QT || RS, PQ = 6, QR = 1.5 and PT = 12. Find ST.STtype your answer...units

Answer 1

`ST=3\text{ units}`

Step-by-step explanation:

Let x represent the length of segment ST.

Given that the lines QT and RS are parallel, the, then the triangles QPT and RPS are similar.

So, the ratio of their sides will be equal;

`(QP)/(PT)=(RP)/(PS)`

Given;

`\begin{gathered} QP=6 \\ PT=12 \\ RP=6+1.5=7.5 \\ PS=12+x \end{gathered}`

substituting;

`\begin{gathered} (6)/(12)=(7.5)/(12+x) \\ 12+x=(7.5*12)/(6) \\ 12+x=15 \\ x=15-12 \\ x=3 \\ ST=3\text{ units} \end{gathered}`

Therefore;

`ST=3\text{ units}`