Question

please answer this quick

Answer 1

PA/AQ=PB/BR=3
reciprocating
AQ/PA=BR/PB=1/3
adding 1 to all
AQ/PA+1=BR/PB+1=1/3+1
PQ/PA=PR/PB=4/3
reciprocating
PA/PQ=PB/PR=3/4.............................(1)
In △PAB & △PQR
PA/PQ=PB/PR=3/4(From(1))
∠APB=∠QRP(common)
△PAB~△PQR(AA)
(PA/PQ)²= Ar△PAB /Ar△PQR..............................(2)
9/16=Ar△PAB /32(Ar△PQR=32cm²)
18cm²=Ar△PAB ...................(3)
In (2)
(PA/PQ)²= Ar△PAB /Ar△PQR
9/16=Ar△PAB /Ar△PQR
reciprocating
16/9=Ar△PQR/Ar△PAB
subtracting 1 from both sides
16/9-1= Ar△PQR/Ar△PAB-1
16-9/9=Ar△PQR- Ar△PAB/Ar△PAB
7/9=Ar ABQR/Ar△PAB
7/9=Ar ABQR/18(from(3))
14cm²=Ar ABQR