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
Let's let the width be represented by "w" meters.
According to the given information, the length of the rectangle is four meters less than twice its width. Thus, the length can be represented as 2w - 4.
We can now set up an equation using the formula for the area of a rectangle:
Area = Length * Width
96 = (2w - 4) * w
96 = 2w^2 - 4w (distributing)
2w^2 - 4w - 96 = 0 (subtracting 96 from both sides)
Now, we can solve this quadratic equation to find the value(s) of "w" that satisfy it.
We can solve this problem by setting up an equation using the given information.
Let's start by defining the width of the rectangle as "w" meters.
The length of the rectangle is four meters less than twice its width. So, the length would be (2w - 4) meters.
The formula for the area of a rectangle is length times width:
Area = Length * Width
We know that the area of the rectangle is 96 m^2, so we can substitute the values into the equation:
96 = (2w - 4) * w
Now we can solve this equation to find the value of "w" (width) and then find the length.
Expanding the equation, we get:
96 = 2w^2 - 4w
Rearranging the equation and setting it equal to zero:
2w^2 - 4w - 96 = 0
Factoring out a 2 from the equation:
2(w^2 - 2w - 48) = 0
Now we can factor the quadratic equation:
(w - 8)(w + 6) = 0
Setting each factor equal to zero:
w - 8 = 0 or w + 6 = 0
w = 8 or w = -6
Since the width cannot be negative, we discard w = -6.
Therefore, the width of the rectangle is 8 meters.
To find the length, we substitute the value of "w" into the expression for the length:
Length = 2w - 4
Length = 2(8) - 4
Length = 16 - 4
Length = 12 meters
So, the length of the rectangle is 12 meters and the width is 8 meters.