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} 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  Algebra House
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