The area of a rectangle is 77 ft², and the length of the rectangle is 3 ft more than twice the width. Find the dimensions of the rectangle.
w = width
2w + 3 = length {length is 3 more than twice the width} Area of a rectangle = width x length w(2w + 3) = 77 {area is width x length} 2w² + 3w = 77 {used distributive property} 2w² + 3w  77 = 0 {subtracted 77 from each side} 2w + 14w  11w  77 = 0 {split 3w into 2 terms who’s coefficients multiply to get 154 and add to get 3} 2w(w + 7)  11(w + 7) = 0 {factored 2w out of first two terms and 11 out of last two terms} (2w  11)(w + 7) = 0 {factored (w + 7) out of the two terms} 2w  11 = 0 or w + 7 = 0 {set each factor equal to zero} 2w = 11 or w = 7 {added 11 to each side of first equation, and subtracted 7 from each side of second equation} w = 11/2 {width cannot be 7} w = 5.5 ft {changed to decimal} 2w + 3 = 14 {substituted 5.5, in for w, into 2w + 3} width = 5.5 ft length = 14 ft Ask the House
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