SOLUTION: The length of a rectangle is 7 inches longer than it is wide. If the area is 198 square inches, what are the dimensions of the rectangle?

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Question 975767: The length of a rectangle is 7 inches longer than it is wide. If the area is 198 square inches, what are the dimensions of the rectangle?
Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
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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