In a scalene triangle ABC , AD and CF are the altitudes drawn from A and C on the sides BC and AB respectively. If the area of the triangle ABC and BDF are 18sq.units and 2 sq. units respectively and DF = `2sqrt2` , then R =

Options

A. `9/4`
B. `9/2`
C. 9
D. none of these

Explanation

We have,
Area of `DeltaBDF`=2 sq. units
`therefore1/2xxBDxxBFsinB=2`

`rArr1/2(ccosB)(acosB)sinB=2`
`rArr1/2a ccos^(2)BsinB=2`
`rArr(1/2acsinB)cos^(2)B=2`
`rArr` (Area of `Delta` ABC)`cos^(2)B=2`
`rArr18cos^(2)B=2rArrcosB=1/3rArrsinB=(2sqrt2)/3`
we have,
`DF=2sqrt2`
`rArrbcosB=2sqrt2rArrb/3=2sqrt2rArrb=6sqrt2`
`thereforeR=b/(2sinB)rArrR=(6sqrt2)/(2xx(2sqrt2)/3)=9/2` units