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QP=24 cm
RS=11.25 cm
QS=18.75 cm
Explanation:
Given that TQ bisects [tex]therefore consider ΔRQS and ΔRPT QS||PT,RP and RT are transversals [tex] comparing (1) and (2) [tex] Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle) Therefore therefore by AA criterion for similarity ΔRQS~ΔRPT According to the property of similar triangles [tex]RQ/RP=RS/RT=QS/PT[/tex][tex]9/RP=X/30=QS/50\\9/RP=X/30=(30-X)/50\\X/30=(30-X)/50\\50X=30(30-X)\\50X=900-30X\\50X+30X=900\\80X=900\\X=900/80=11.25\\RS=11.25 cm\\QS=30-X=30-11.25\\QS=18.75 cm\\9/RP=X/30\\9/RP=11.25/30\\9*30/11.25=RP\\RP=24 cm[/tex]
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