The length of a rectangle is 2 less than 3 times its width. If the area of the rectangle is 96cm², what is the length of the rectangle?

Answer: The length is 16 cm

Step-by-step explanation:

L = 3w - 2 w * L = 96 substitute for L

w (3w - 2) = 96

3w² - 2w = 96

3w² - 2w - 96 = 0 factor this

(3w + 16) (w - 6) = 0 Set the w-6 factor equal to 0 and solve for w (The 3w + 16 will yield a negative number; real rectangles can't have negative dimensions!)

w-6 = 0 so w = 6

Original equation for L L = 3w - 2 substitute 6 for w

L = 3 (6) - 2 = 18 - 2

L = 16