SOLUTION: The length of a rectangle is 1 ft. more than twice its width, and the area of the rectangle is 45 ft. ^2 . Find the dimensions of the rectangle..
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Question 767530: The length of a rectangle is 1 ft. more than twice its width, and the area of the rectangle is 45 ft. ^2 . Find the dimensions of the rectangle.. Answer by algebrahouse.com(1659) (Show Source):
A = lw {area of a rectangle}
x(2x + 1) = 45 {substituted width and length into area formula}
2x² + x = 45 {used distributive property}
2x² + x - 45 = 0 {subtracted 45 from each side}
2x² + 10x - 9x - 45 = 0 {split the x into 10x and -9x using factoring by grouping}
2x(x + 5) - 9(x + 5)= 0 {factored 2x out of first two terms and -9 out of last two terms}
(2x - 9)(x + 5) = 0 {factored (x + 5) out of the two terms}
2x - 9 = 0 or x + 5 = 0 {set each factor equal to 0}
2x = 9 or x = -5 {added 9 and subtracted 5}
x = 9/2 or x = -5 {divided first equation by 2}
x = 9/2 {width cannot be negative}
2x + 1 = 10 {substituted 9/2, in for x, into 2x + 1}
