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

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

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