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___
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___
Let the width of the rectangle be x meters.
The length of the rectangle is then 2x - 4 meters.
The formula for the area of a rectangle is A = length * width.
Substituting the given values, we have 96 = (2x - 4) * x.
To solve this equation, we can simplify it and set it equal to zero.
Rearranging, we get 2x^2 - 4x - 96 = 0.
Using trial and error or factoring, we find that (x - 8)(2x + 12) = 0.
This gives us two possible solutions: x = 8 or x = -6.
Since the width cannot be negative, we discard the second solution.
Thus, the width of the rectangle is 8 meters.
Plugging this value back into the expression for the length, we find that the length is 2(8) - 4 = 12 meters.
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.