Answer:
Let's call the length of the rectangle "L" and the width "W".
From the problem, we know that:
W = L - 4
And
Area = Length x Width
Substituting the first equation into the second equation, we get:
Area = L x (L - 4)
We also know that the area is 21 square units, so we can set up the following equation:
21 = L x (L - 4)
Expanding the right side of the equation:
21 = L^2 - 4L
Rearranging the terms:
L^2 - 4L - 21 = 0
Now we can solve for L using the quadratic formula:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -4, and c = -21
L = (-(-4) ± sqrt((-4)^2 - 4(1)(-21))) / 2(1)
L = (4 ± sqrt(100)) / 2
L = (4 ± 10) / 2
L = 7 or L = -3
Since the length cannot be negative, we choose L = 7.
Therefore, the length of the rectangle is 7 units.