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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

5 answers

To express the length of the rectangle in terms of its width, we can use the information given:

Let the width be denoted as \( w \).

According to the problem, the length \( l \) of the rectangle is four meters less than twice its width. This relationship can be expressed mathematically as:

\[ l = 2w - 4 \]

So, the expression for the length of the rectangle in terms of the width is:

2w - 4.

Next, we can use the area of the rectangle to find the values of width and length. The area \( A \) of a rectangle is given by the formula:

\[ A = l \times w \]

We know the area is 96 m², so:

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

Expanding this equation gives:

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

Rearranging to set the equation to zero:

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

Dividing the entire equation by 2 simplifies it:

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

Now, we can factor this quadratic equation:

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

Setting each factor to zero gives:

  1. \( w - 8 = 0 \) → \( w = 8 \)
  2. \( w + 6 = 0 \) → \( w = -6 \) (not a valid solution since width can't be negative)

Thus, the width \( w \) is 8 m.

Now, substitute back to find the length:

\[ l = 2(8) - 4 = 16 - 4 = 12 \]

So, the dimensions of the rectangle are:

Width = 8 m Length = 12 m

An expression for the length of the rectangle in terms of the width would be, (What?)

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

The formula for the area of a rectangle is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

In mathematical notation, it can also be expressed as:

\[ A = l \times w \]

where \( A \) is the area, \( l \) is the length, and \( w \) is the width of the rectangle.