Question 975767
w = width
w + 7 = length {length is 7 longer than the width}


Area of a rectangle = width x length


w(w + 7) = 198 {substituted width and length into area formula}
w² + 7w = 198 {used distributive property}
w² + 7w - 198 = 0 {subtracted 198 from each side}
(w + 18)(w - 11) = 0 {factored into two binomials}
w + 18 = 0 or w - 11 = 0 {set each factor equal to 0}
w = -18 or w = 11 {solved each equation for w}
w = 11 {width cannot be negative}
w + 7 = 18 {substituted 11, in for w, into w + 7 to find the length}


width = 11 inches
length = 18 inches
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