area of a rectangle=base x height
perimeter of a rectanble=2(base)+2(height)
base=x
height=y
we have to compute this system of equations:
xy=45
2x+2y=28
We solve this system by substitution method
xy=45 ⇒x=45/y
2(45/y)+2y=28
90/y + 2y=28
90+2y²=28y
2y²-28y+90=0
we divide each factor by "2" to simplify
y²-14y+45=0
We solve this quadratic equation:
y=[14⁺₋√(196-180)]/2
y=(14⁺₋4)/2
we have two solutions
y₁=9 ⇒x₁=45/9=5
y₂=5 ⇒x₂=45/5=9
Answer: the dimensions fo the paper are 5 x 9