It is obvious that angles

*
and also
*
room equal in both triangles. This method that the connection PT/PQ = RT/RS and TQ/PQ = TS/RS should be fulfilled. Replacing with data (units are omitted)

30/PQ = 35/RS

30/35 = PQ/RS

PQ/RS = 0.857

60/PQ = (60 + QS)/RS

60/(60 + QS) = PQ/RS

60/(60 + QS) = 0.857

60 = 0.857*(60 + QS)

60 - 0.857*60 = 0.857*QS

QS = (60 - 0.857*60)/0.857

QS = 10

*


Option C 10 cm

Step-by-step explanation:

we understand that

If 2 triangles are similar, then the ratio of its matching sides is proportional

In this problem

Triangles PTQ and RTS space similar

therefore

PT/RT=QT/TS

we have

PT=30 cm

RT=PT+RP=30+5=35 cm

QT=60 cm

TS=SQ+QT=SQ+60

substitute

30/35=60/(SQ+60)

Solve for SQ

30(SQ+60)=35*60

SQ+60=70

SQ=70-60=10 centimeter




*

*

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