Question

In Given Fig AB=120, BC=90 CD=60 PS=360, Seg PA, Seg QB, Seg RC, Seg SD are all perpendicular to seg AD. Find A. PQ B. QR C. RS​

Answer 1

Given:

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

To find: PQ, QR & RS

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

Proof: In ΔEDS,

AP║ BQ║DS║CR [ given]

PQ : QR: RS = AB:BC:CD

[By using BPT]

PQ : QR: RS = 60:70:80

Let PQ= 60x , QR= 70x RS= 80x

PS = PQ+QR+RS

PQ+QR+RS= 280 [PS=280cm]

60x+70x+80x=280

210x=280

x= 280/210 = 4/3

x=4/3

PQ= 60x = 60× 4/3= 80cm

QR= 70x = 70× 4/3= 280/3

RS= 80x= 80× 4/3= 320/3cm

Hence PQ= 80cm , QR= 280cm, RS=320cm

HOPE THIS WILL HELP YOU