Question 465880: the length of a rectangle is 2 inches longer than its width. the area of the rectangle is 323 in2. find the demensions of the rectangle.
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! "the length of a rectangle is 2 inches longer than its width. the area of the rectangle is 323 in2. find the demensions of the rectangle."
x = width
x + 2 = length {length is 2 longer than width}
Area of a rectangle is width x length
x(x + 2) = 323 {area is width x length}
x² + 2x = 323 {used distributive property}
x² + 2x - 323 = 0 {subtracted 323 from both sides}
(x + 19)(x - 17) = 0 {factored into two binomials}
x + 19 = 0 or x - 17 = 0 {set each factor equal to 0}
x = -19 or x = 17 {subtracted 19 and added 17, respectively}
x = 17 {width cannot be negative}
x + 2 = 19 {substituted 17, in for x, into x + 2}
width = 17 in. and length = 19 in.
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