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

Explanation

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`