Question 429003: The area of a rectangle is 80 meters. the length is one more than three times the width. Find the dimensions of the rectangle.
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website! "The area of a rectangle is 80 meters. the length is one more than three times the width. Find the dimensions of the rectangle."
x = width
3x + 1 = length {length is one more than three times width}
Area of a rectangle = length x width
x(3x + 1) = 80 {area is length x width}
3x^2 + x = 80 {used distributive property}
3x^2 + x - 80 + 0 {subtracted 80 from both sides to get into standard form}
(3x + 16)(x - 5) = 0 {factored into two binomials}
3x + 16 = 0 or x - 5 = 0 {set each factor equal to 0}
3x = -16 or x = 5 {subtracted 16 and added 5, respectively}
x = -16/3 or x = 5 {divided left equation by 3}
x cannot be negative, it is the width of a rectangle
x = 5
3x + 1 = 16 {substituted 5, in for x, into 3x + 1}
width = 5 m and length = 16 m
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