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 Response area
Using trial and error, if the area is 96 m^2, then the length and width are
To find the length (L) and width (W) of the rectangle, you can use the given information that the length is four meters less than twice the width.
Expression for the length in terms of the width:
L = 2W - 4
Formula for the area of a rectangle:
Area = Length * Width
Since the area is given as 96 m^2, you can substitute the expressions for length and width into the formula:
96 = (2W - 4) * W
Now, you can solve this equation for W:
96 = 2W^2 - 4W
2W^2 - 4W - 96 = 0
This is a quadratic equation. To solve it, you can either factor it or use the quadratic formula. Factoring this equation gives:
(W - 8)(2W + 12) = 0
Setting each factor equal to zero:
W - 8 = 0 or 2W + 12 = 0
Solving these equations, you get:
W = 8 or W = -6
Since the width cannot be negative, the width of the rectangle is 8 meters.
To find the length, you can substitute the width into the expression for the length:
L = 2W - 4
L = 2 * 8 - 4
L = 16 - 4
L = 12
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
what is the area formula?
The formula for the area of a rectangle is:
Area = Length * Width