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Since ( PQ ) is parallel to ( RS ), we can use the properties of similar triangles to find the length of ( SQ ). The segments ( RP ), ( PT ), and ( QT ) are proportional. The total length ( RT ) is ( RP + PT = 6 , \text{cm} + 18 , \text{cm} = 24 , \text{cm} ). Using the proportionality, we have:

[ \frac{SQ}{QT} = \frac{RP}{RT} \Rightarrow SQ = QT \cdot \frac{RP}{RT} = 21 \cdot \frac{6}{24} = 5.25 , \text{cm. }]

Thus, the length of ( SQ ) is ( 5.25 , \text{cm} ).

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