2. The length of a rectangle is four meters less than twice its width.

Question

2.  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 Response area

GPT-4o mini · Answer

To solve this problem, we can break it down into parts.

Express the length in terms of the width: The problem states that the length (L) is four meters less than twice the width (W). This can be expressed mathematically as: \[ L = 2W - 4 \]
Formula for the area of a rectangle: The area (A) of a rectangle is calculated as: \[ A = Length \times Width = L \times W \] Substituting for the length in terms of width gives: \[ A = (2W - 4) \times W \]
Set the area equal to 96 m²: Since the area is given as 96 m², we can set up the equation: \[ (2W - 4) \times W = 96 \] This simplifies to: \[ 2W^2 - 4W - 96 = 0 \]
Simplifying the equation: We can divide the entire equation by 2: \[ W^2 - 2W - 48 = 0 \]
Solving the quadratic equation: We can factor this equation: \[ (W - 8)(W + 6) = 0 \] This gives us two possible solutions: \[ W = 8 \quad \text{or} \quad W = -6 \] Since width cannot be negative, we take \(W = 8\) m.
Finding the length: Now, substitute \(W\) back to find the length: \[ L = 2(8) - 4 = 16 - 4 = 12 \text{ m} \]

So, the final answers are:

Width: 8 m
Length: 12 m

Responses:

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 L × W.
Using trial and error, if the area is 96 m², then the length and width are Length = 12 m and Width = 8 m.