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Question 14
In figure , PA, QB, RC and SD are all perpendiculars to a line l, AB = 6cm, BC = 9cm, CD = 12cm and SP = 36cm. Find PQ, QR and RS.

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Solution

Given, AB =6cm, BC = 9cm, CD = 12cm and SP = 36cm.

Also, PA, QB, RC and SD are all perpendiculars to line l.
PA II QB II RC II SD
By basic proportionality theorem,
PQ:QR:RS = AB:BC:CD = 6:9:12
Let PQ = 6x, QR = 9x and RS = 12x
Since, length of PS = 36 cm
PQ + QR + RS = 36
6x + 9x + 12x = 36
27x = 36
x=3627=43
Now, PQ=6x=6×43=8cm
QR=9x=9×43=12cm
and RS=12x=12×43=16cm

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