Question

In the given figure, each of PA, QB, RC and SD is perpendicular to l. If AB = 6 cm, BC = 9 cm, CD = 12 cm and PS = 36 cm, then determine PQ, QR and RS.

Answer 1

Answer:

PQ = 8cm , QR =12cm &  RS =16cm.

Step-by-step explanation:

Given:

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

AB = 6 cm ,  BC = 9 cm,   CD = 12 cm, PS = 36 cm.

To find : PQ, QR & RS

Proof :  

AP║ BQ║DS║CR        [ given]

∴ PQ : QR : RS  = AB : BC : CD

[By intercepts theorem : If three or more parallel lines are intersected by transversal then the intercept made by them on the transversals are proportional]

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

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 =16cm.

HOPE THIS ANSWER WILL HELP YOU ..

Answer 2

Answer:pq=8cm

Qr=12cm and Rs=16cm