Ask a New Question
Menu

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)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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?

1 answer

To solve the problem step by step:

  1. Expression for the length of the rectangle in terms of the width:

    • Let the width be \( w \).
    • Given that the length is four meters less than twice the width, the expression for the length \( l \) is: \[ l = 2w - 4 \]

  2. Formula for the area of a rectangle:

    • The area \( A \) of a rectangle is given by the formula: \[ A = l \times w \]

  3. Using the area of the rectangle to find the dimensions:
    Since the area is given as 96 m², we can set up the equation: \[ A = (2w - 4) \times w = 96 \]

    Simplifying this: \[ 2w^2 - 4w = 96 \] Rearranging gives: \[ 2w^2 - 4w - 96 = 0 \] Dividing through by 2 simplifies it to: \[ w^2 - 2w - 48 = 0 \] Now we will factor the quadratic: \[ (w - 8)(w + 6) = 0 \] Setting each factor to zero gives us: \[ w - 8 = 0 \quad \text{or} \quad w + 6 = 0 \] Thus, \( w = 8 \) (valid, since width can't be negative) or \( w = -6 \) (invalid).

    So, the width \( w = 8 \) meters. Now, substituting \( w \) back to find length \( l \): \[ l = 2(8) - 4 = 16 - 4 = 12 \text{ meters} \]

  4. Conclusion:

    • The width is 8 meters.
    • The length is 12 meters.

Now, we can fill in the responses for your specific input sections:

  • 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: A = l × w
  • Using trial and error, if the area is 96 m², then the length and width are: Length = 12 m, Width = 8 m.