In adjoining figure seg PS perpendicular seg RQ, seg QT perpendicular seg PR. if RQ=6, PS=12, Then find QT
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Answer:
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…
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