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

Given  `AB = 6cm ,BC = 9cm,CD= 12cm,AD=27cm ` and `PS = 36cm`

PA, QB, RC and SD is perpendicular to l,

Therefore, by the corollory of basic proportionality theorem, we have

`(AB)/(AD)=(PQ)/(PS)`

`(BC)/(AD)=(QR)/(PS)`

`(CD)/(AD)=(RS)/(PS)`

`⇒ (AB)/(AD)=(PQ)/(PS)`

`6/27=(PQ)/36`

`(6xx36)/27=PQ`

`PQ = 8`

Now for QR

`(BC)/(AD)=(QR)/(PS)`

`(9)/(27)=(QR)/(36)`

`(6xx36)/27=QR`

`QR=12`

Again for RS

`(CD)/(AD)=(RS)/(PS)`

`12/27=(RS)/36`

`(12xx36)/27=RS`

`RS = 16`

Hence, the values of PQ, QR and RS are `8,12,16`respectively.