14 In Fig. 6.21, PA, QB Rc and SD are all perpendiculars to a line l, – InterviewSolution

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1.	14 In Fig. 6.21, PA, QB Rc and SD are all perpendiculars to a line l, AB 6 cm, Bc 9 cm, CD g cm and SP 36 om Find PO, QR an RS. Fig. 6.21
Answer» Given,AB=6 cm, BC= 9 cm, CD= 12 cm and SP = 36 cm Also, PA. QB,RC and SD are alll perpendiculars to line l `therefore PAabs()QBabs()RCabs()SD` By basic proportionality theorem, PQ : QR : RS = AB : BC : CD =6 : 9 : 12 Let PQ=6x,QR=9x and RS=12 x Since length of PS = 36 km `thereforePQ+QR+RS=36` `rArr6x+9x+12x=36` `rArr 27x = 36` `therefore x=36/27=4/3` Now, PQ=`6x=6xx4/3=8cm` QR=`9x=9xx4/3=12 cm` and RS=12 x =`12xx4/3=16 cm`

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