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.

Answer 1

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