Question

Please solve q 37 ?

Answer 1

`2sqrt21`

Explanation:

Let `|ABC|` denote area of `DeltaABC`,
let `AD=y, and DC=x`,
`=> |ADP|=1/2*y*AP=5, => AP=10/y, => PB=x-10/y`
`|DQC|=1/2*x*QC=3, => QC=6/x, => BQ=y-6/x`
`|BPQ|=1/2*(x-10/y)*(y-6/x)=4`
`=> (x-10/y)(y-6/x)=8`
`=> xy^2-24xy+60=0`
`=> xy=(24+-sqrt(24^2-4xx60))/2`
`=> xy=12+-2sqrt21`
As `xy=|ABCD|, and xy > (3+4+5) = 12`,
`=> xy=12+2sqrt2`
`=> |DPQ|=12+2sqrt21-(3+4+5)=2sqrt21 " unit"^2`