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Question
In figure, PA, QB, RC and SD are all perpendiculars to a line l, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm. Find PQ, QR and RS.
Solution
Given, AB = 6 cm, BC = 9 cm, CD = 12 cm and SP = 36 cm
Also, PA, QB, RC and SD are all perpendiculars to line l
∴ PA || QB || RC || 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 = `36/27 = 4/3`
Now, PQ = 6x
= `6 xx 4/3`
= 8 cm
QR = 9x
= `9 xx 4/3`
= 12 cm
And RS = 12x
= `12 xx 4/3`
= 16 cm
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