Please solve q 37 ?

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1 Answer
CW
May 12, 2018

2sqrt212√21

Explanation:

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Let |ABC||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

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