Question

If PA , QB , RC and SD are all perpendiculars to a line L , AB =6cm , BC =9cm ,CD=12cm and SP =36 cm. Find PQ, QR and RS.

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 = 4/3

x = 4/3

∴ PQ = 6x = 6× 4/3

PQ = 8cm

QR = 9x = 9 × 4/3

QR= 12cm

RS = 12x = 12× 4/3

RS = 16 cm

Hence PQ = 8cm , QR = 12cm,   RS = 16 cm

Hope this will help you.....

Answer 2

Step-by-step explanation:

here is ur answer bro jai hind vandematram