Question

The length of a rectangular field is 20 less than its width. The area of the field is 12,000 ft2. What is the width of the field?

Answer 1

If length is x and width is y:

(1) x = y - 20
(2) Area = xy
12 000 = xy

Now if we substitute equation (1) into (2) we get:
12 000 = y(y - 20)
y^2 - 20y - 12 000 = 0
(y - 10)^2 - 100 - 12 000 = 0
(y - 10)^2 - 12 100 = 0
(y - 10 + 110)(y - 10 - 110) = 0
(y + 100)(y - 120)
y = -100 or y = 120
Since y is a length and cannot be negative, y = 120 ft

Answer 2

Let the width be x.
width = x
Length = x - 20

Area = 12000
x(x -20) = 12000
x² - 20x - 12000 = 0
(x+100)(x-120) = 0
x = -100 (rejected, length cannot be negative) or x = 120

Width = x = 120
Length = x - 20 = 120 - 20 = 100

Answer: Width = 120 ft