Question

In the given figure pa qb and rc are perpendicular to l if ab = 6cm

Answer 1

Given:

PA, QB, RC,& SD are perpendicular on line l.

To find: PQ, QR & RS

Construction: produce SP  & l to meet each other at E.

Proof: In ΔEDS,
AP║ BQ║DS║CR        [ given]

∴ PQ : QR: RS  = AB:BC:CD

PQ : QR: RS = 6:9:12

let PQ= 6x  , QR= 9x    RS= 12x

PS = PQ+QR+RS

∴ PQ+QR+RS=36                   [PS=36cm]

6x+9x+12x=36

27x=36

x= 36/27= 3/4

x=3/4

∴ PQ= 6x = 6× 4/3= 8cm

QR= 9x = 9 × 4/3= 12cm

RS= 12x= 12× 4/3= 16 cm

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Hence PQ= 8cm , QR=12cm,   RS=16cm
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Hope this will help you...