The area of a rectangle is 14ft^2, and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
Let the width of the rectangle be w.
Given that the length of the rectangle is 3ft less than twice the width, we can write the length as 2w - 3.
The area of a rectangle is given by the formula: Area = length x width
Thus, we have the equation: 14 = (2w - 3)w
Expanding and setting the equation equal to zero, we get: 2w^2 - 3w - 14 = 0
Now, we can solve this quadratic equation using the quadratic formula: w = (-(-3) ± √((-3)^2 - 4(2)(-14))) / 2(2)
w = (3 ± √(9 + 112)) / 4
w = (3 ± √121) / 4
w = (3 ± 11) / 4
w = 14/4 or w = -8/4
w = 3.5 or w = -2
Since the width of the rectangle cannot be negative, the width is 3.5 ft.
Now, substitute the width back into the expression for the length: length = 2(3.5) - 3 = 7 - 3 = 4 ft
Therefore, the dimensions of the rectangle are width = 3.5 ft and length = 4 ft.