The area of PQRS is equal to the area of rectangular ABCD minus four triangles DRS, RCQ, QDB and SAD.
The area of DRS =DR*DS/2=x(8-x)/2.
RCQ=CR*CQ/2=( 10-x)x/2
QPB=BQ*PB/2=(8-x)x/2
SAP=SA*AP/2==( 10-x)x/2
Area of ABCD = 10*8=80.
therefore
The area of PQRS = 80-[x (8-x)/2+(10-x) x/2+x (8-x)/2+(10-x) x/2]
=80-[x(8-x)+( 10-x)x]
=80-( 18x-2x square)
=2x squared-18x+80
Because it is known that the area of PQRS is the square of A=2X-18X+80.
therefore
2X squared-18X+80=2x squared-18X+80
For any x, the equation holds.
Because x is the length
So x & gt=0.
And because 8-x, 10-x is the length, >; =0
So x < =8
Therefore {x | 0