The length of a rectangular piece of carpet is 2 meters less than 5 times its width. Find the dimensions of the carpet if its area is 16 square meters. Solve algebraically.

**w = width**

5w - 2 = length{length is 2 less than 5 times width}

5w - 2 = length

**Area of a rectangle = length x width**

w(5w - 2) = 16 {substituted length, width, and given area into area formula}

5w² - 2w = 16 {used distributive property}

5w² - 2w - 16 = 0 {subtracted 16 from each side}

5w² - 10w + 8w - 16 = 0 {split -2w into -10w and 8w, factoring by grouping}

5w(w - 2) + 8(w - 2) = 0 {factored 5w out of first two terms and 8 out of last two terms}

(5w + 8)(w - 2) = 0 {factored out the common factor of the two terms, (w - 2)}

5w + 8 = 0 or w - 2 = 0 {set each factor equal to 0}

w = -8/5 ow w = 2 {solved each equation}

w = 2 {width cannot be negative}

5w - 2 = 8 {substituted 2, in for w, into 5w - 2}

**width = 2m**

length = 8m

length = 8m

*- Algebra House*