Question

The area of a rectangular piece of paper is 45 square inches. the perimeter is 28 inches. What are the dimensions of the paper?

Answer 1

5 and 9, because 5X9= 45, and 5+5+9+9= 28

Answer 2

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