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

Width of the rectangle is 9 units

Step-by-step explanation:

Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length * width

⇒54 = x (x - 3)

⇒54 = x² - 3x

⇒x² - 3x - 54 = 0

⇒x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

⇒x (x + 6) - 9 (x + 6) = 0

⇒ (x + 6) (x - 9) = 0

⇒x = - 6, 9 (negative value is neglected)

x = 9 units

9 units

Step-by-step explanation:

Area of rectangle=L*W

L=w-3, w (w-3)

w^2-3w=54

w=9