The width of a rectangle is 3 units less than the length. The area of the rectangle is 54 units. What is the length, in units of the rectangle?

9 units

Step-by-step explanation:

length: L

Width: L - 3

Area = length * width

(L - 3) * L = 54

L² - 3L - 54 = 0

L² - 9L + 6L - 54 = 0

L (L - 9) + 6 (L - 9) = 0

(L - 9) (L + 6) = 0

L = 9, - 6

L = 9

The length is 9 units

Step-by-step explanation:

Let x = length

width = x-3

Area = 54 = l*w

54 = x * (x-3)

Distribute

54 = x^2 - 3x

Subtract 54 from each side

54-54 = x^2 - 3x-54

0 = x^2 - 3x-54

Factor

What 2 number multiply to - 54 and add to - 3

-9 * 6 = 54

-9+6 = -3

(x-9) (x+6) = 0

Using the zero product property

x=9 x=-6

Since we cannot have negative length

x=9 units

The length is 9 units