The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 square meters, what is the length and the width?
(3 points)
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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 96m^2, then the length and width are Response area
An expression for the length of the rectangle in terms of the width would be 2w - 4.
The formula for the area of a rectangle is Area = length * width.
Using trial and error, if the area is 96m^2, then the length and width are 12m and 8m.
To find the length and width of the rectangle, we can set up an equation using the given information.
Let's denote the width of the rectangle as 'w' meters.
According to the given information, the length of the rectangle is four meters less than twice its width. So, the length can be expressed as 2w - 4.
The formula for the area of a rectangle is length multiplied by width.
Area = length * width
Substituting the values into the formula, we get:
96 = (2w - 4) * w
Now, we can solve this equation to find the value of 'w', which represents the width of the rectangle.
To solve the equation, we can simplify it first:
96 = 2w^2 - 4w
Next, let's rearrange the equation to bring all terms to one side and set it equal to zero:
2w^2 - 4w - 96 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's use the quadratic formula:
w = (-(-4) ± √((-4)^2 - 4(2)(-96))) / (2(2))
w = (4 ± √(16 + 768)) / 4
w = (4 ± √784) / 4
w = (4 ± 28) / 4
Simplifying further, we have:
w = (4 + 28) / 4 or w = (4 - 28) / 4
w = 32 / 4 or w = -24 / 4
w = 8 or w = -6
Since the width of a rectangle cannot be negative, we discard the value w = -6.
Therefore, the width of the rectangle is 8 meters.
To find the length, we can substitute the value of the width into the expression we found earlier: 2w - 4.
Length = 2(8) - 4 = 16 - 4 = 12 meters.
So, the length of the rectangle is 12 meters and the width is 8 meters.
An expression for the length of the rectangle in terms of the width would be (2w-4).
The formula for the area of a rectangle is length times width (A = l * w).
Using trial and error, if the area is 96m^2, then the length and width are:
Length = 8 meters
Width = 12 meters