n Fig, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm

1.	n Fig, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm,D 12 cm and SP 36 cm. Eind PQ, QR and RS.
Answer» 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: InΔEDS,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

n Fig, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm,D 12 cm and SP 36 cm. Eind PQ, QR and RS.

Answer»

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: InΔEDS,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