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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.
Solution
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.
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