Find the dimensions of the rectangle

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.

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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

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