In the figure, PQ is parallel to RS. The length of RP is 2 cm; the length of PT is 18 cm; the length of QT is 27 cm. What is the length of SQ?

Step 1    Find the value of TSwe know thatif PQ is parallel to RS. then triangles TRS and TPQ are similarso[tex]\frac{TR}{TP} =\frac{TS}{QT}[/tex]solve for TS[tex]TS =\frac{TR*QT}{TP}[/tex]we have[tex]RP=2\ cm\\TP=18\ cm\\QT=27\ cm[/tex][tex]TR=TP+RP\\TR=18+2=20\ cm[/tex]substitute[tex]TS =\frac{20*27}{18}[/tex]  [tex]TS =30\ cm[/tex]Step 2Find the value of SQwe know that[tex]SQ=TS-QT[/tex]we have[tex]TS =30\ cm[/tex][tex]QT=27\ cm[/tex]substitute[tex]SQ=30\ cm-27\ cm=3\ cm[/tex]thereforethe answer isthe value of SQ is [tex]3\ cm[/tex]