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?
(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 Response area
Using trial and error, if the area is 96 m^2, then the length and width are
Let's say the width of the rectangle is x meters. According to the problem, the length is four meters less than twice the width, which can be expressed as 2x - 4.
Now, let's find the area of the rectangle using the formula: Area = length * width. Therefore, Area = (2x - 4) * x.
We are given that the area is 96 m², so we can set up the equation: (2x - 4) * x = 96.
Simplifying the equation, we get: 2x² - 4x = 96.
Subtracting 96 from both sides: 2x² - 4x - 96 = 0.
Now, we can factor the equation: 2(x - 8)(x + 6) = 0.
Setting each factor equal to zero, we find two solutions: x - 8 = 0 and x + 6 = 0.
Solving for x in each case, we find x = 8 and x = -6. Since the width cannot be negative, we discard the solution x = -6.
Therefore, the width of the rectangle is 8 m.
To find the length, we substitute this width value into the expression for the length: Length = 2x - 4 = 2(8) - 4 = 16 - 4 = 12 m.
So, the length of the rectangle is 12 m and the width is 8 m.
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 x width.
Using trial and error, we can find that if the area is 96 m^2, then the length and width are:
Length = 12 meters
Width = 8 meters.