Question 816082
x = width
2x - 3 = length {length is 3 less than double the width}


Area of a rectangle = width x length


x(2x - 3) = 27 {substituted width, length, and area into area formula}
2x² - 3x = 27 {used distributive property}
2x² - 3x - 27 = 0 {subtracted 27 from each side}
2x² - 9x + 6x - 27 = 0 {split -3x into two terms whose coefficients multiply to get -54 and add to get -3}
x(2x - 9) + 3(2x - 9) = 0 {factored x out of first two terms and 3 out of last two terms}
(2x - 9)(x + 3) = 0 {factored (2x - 9) out of the two terms}
2x - 9 = 0 or x + 3 = 0 {set each factor equal to 0}
2x = 9 or x = -3 {added 9 in first equation, subtracted 3 in second equation}
x = 4.5 {divided first equation by 2, the width cannot be negative, so -3 is out}
2x - 3 = 6 {substituted 4.5, in for x, into 2x - 3}


width is 4.5 yds
length is 6 yds
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