Question

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 _____________. 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 ______________.
Fill in the blanks
Options: area = 1/2 (l x w), l = 24 & w = 4, l = 2w - 4, w = 2l - 4, l = 8 & w = 12, l = 12 & w = 8, area = 2l + 2w, l = 4 & w = 24, area = l x w, l = 4 - 2w

Answer 1

are you sure this is correct

Answer 2

Let's fill in the blanks step by step.

1. The expression for the length of the rectangle in terms of the width would be **l = 2w - 4**.
2. The formula for the area of a rectangle is **area = l x w**.
3. Using trial and error, if the area is 96 m², then the length and width are **l = 12 & w = 8**.

So the completed blanks are:

1. An expression for the length of the rectangle in terms of the width would be **l = 2w - 4**.
2. The formula for the area of a rectangle is **area = l x w**.
3. Using trial and error, if the area is 96 m², then the length and width are **l = 12 & w = 8**.

Answer 3

Yes, let's verify the solution step by step to ensure accuracy.

1. **Expression for Length in Terms of Width**:
Given that the length of the rectangle is four meters less than twice its width, we can express the length \( l \) in terms of the width \( w \):

\[
l = 2w - 4
\]

2. **Formula for Area**:
The area \( A \) of a rectangle is given by the formula:

\[
A = l \times w
\]

3. **Setting Up the Equation**:
We know that the area of the rectangle is 96 m². Substituting the expression for \( l \) into the area formula gives:

\[
A = (2w - 4) \times w
\]
\[
96 = (2w - 4) \times w
\]

Expanding the equation:

\[
96 = 2w^2 - 4w
\]

Rearranging gives:

\[
2w^2 - 4w - 96 = 0
\]

Dividing everything by 2 to simplify:

\[
w^2 - 2w - 48 = 0
\]

4. **Factoring or Using Quadratic Formula**:
We can factor this quadratic equation:

\[
(w - 8)(w + 6) = 0
\]

Thus, the solutions for \( w \) are:

\[
w = 8 \quad \text{or} \quad w = -6
\]

Since width cannot be negative, we have:

\[
w = 8 \, \text{m}
\]

5. **Finding the Length**:
Now we substitute \( w = 8 \) back into the expression for \( l \):

\[
l = 2(8) - 4 = 16 - 4 = 12 \, \text{m}
\]

6. **Conclusion**:
Therefore, the length and width of the rectangle are:

\[
l = 12 \, \text{m}, \quad w = 8 \, \text{m}
\]

So the answers originally provided are indeed correct. The final answers are:

- **Expression for the length**: \( l = 2w - 4 \)
- **Formula for area**: \( \text{area} = l \times w \)
- **Length and width**: \( l = 12 \, \text{m} \) and \( w = 8 \, \text{m} \)