The length of a rectangle is 3 cm less than twice the width. if the area of the rectangle is 54 cm2, what is the width of the rectangle

Make an equation system based on the problem

"The length of a rectangle is 3 cm less than twice the width" could be written as

∴ l = 2w - 3 (first equation)

"The area is 54" could be written as

∴ l * w = 54 (second equation)

Substitute (2w - 3) into l in the second equation

l * w = 54

(2w - 3) * w = 54

2w² - 3w = 54

2w² - 3w - 54 = 0

(2w + 9) (w - 6) = 0

The zeros of the equation

2w + 9 = 0 or w - 6 = 0

w = - 9/2 or w = 6

Because the width couldn't be negative, - 9/2 is excluded from the solution. The width of the rectangle is 6 cm