The length of a rectangle is four meters less than twice its width. If the area of the rectangle is 96 m^2, what is the length and the width? An expression for the length of the rectangle in terms of the width would be Response area The formula for the area of a rectangle is Using trial and error, if the area is 96 m^2, then the length and width are Response area
Let's denote the width of the rectangle as w.
According to the problem, the length of the rectangle is four meters less than twice its width, so the length would be 2w - 4.
The formula for the area of a rectangle is given by length * width, which in this case is:
Area = (2w - 4) * w
To find the values of w and the length that satisfy the problem, we can set up the equation:
96 = (2w - 4) * w
Now, we can solve this equation for w.
Expanding the equation:
96 = 2w^2 - 4w
Rearranging the terms:
2w^2 - 4w - 96 = 0
Now we can solve this quadratic equation. Factoring it would be the easiest method:
2w^2 - 4w - 96 = (2w + 12)(w - 8) = 0
Setting each factor equal to zero:
2w + 12 = 0 or w - 8 = 0
Solving these equations:
2w = -12 or w = 8
Dividing both sides by 2:
w = -6 or w = 8
Since width cannot be negative, the width of the rectangle is 8 meters.
Substituting w = 8 back into the expression for the length:
Length = 2w - 4 = 2(8) - 4 = 12
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.