Please solve q 37 ?

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1 Answer
CW
May 12, 2018

#2sqrt21#

Explanation:

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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#

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