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In the given figure, a triangle `PQR` is drawn to circumscribe a circle of radius `6cm` such that the segments `QT` and `TR` into which `QR` is divided by the point of contact `T`, are of lengths `12cm` and `9cm` respectively. If the area of `DeltaPQR=189cm^(2)` then the length of side `PQ` is

A

`17.5cm`

B

`20cm`

C

`22.5cm`

D

`25cm`

Text Solution

Verified by Experts

`ar(DeltaPQR)=(1)/(2)xx("perimeter of"DeltaPQR)xxr`
`implies189=(1)/(2)xx{(x+12)+(12+9)+(9+x)}xx6`
`impliesx=10.5`
`:.PQ=(x+12)cm=(10.5+12)cm=22.5cm`.
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