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

Question

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

Philoid · Accepted Answer

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 ⎩.

∴ PA:QB:RS = AB:BC:CD

= 6:9:12

Let PQ = 6x, QR = 9x and RS = 12x

Since, length of PS = 36 km

∴ PQ + QR + RS = 36

⇒ 6x + 9x + 12x = 36

⇒ 27x = 36