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

Answer 1

[AI-generated answer — Bot GPT 3.5]

L = 2w - 4

Since the area of a rectangle is given by the formula A = length x width, we can set up the equation:

96 = (2w - 4)w

Now we can solve for the width:

96 = 2w^2 - 4w
2w^2 - 4w - 96 = 0
w^2 - 2w - 48 = 0
(w - 8)(w + 6) = 0

So, w = 8 or w = -6

Since the width cannot be negative, the width is 8 meters.

Now we can find the length:

L = 2(8) - 4
L = 16 - 4
L = 12 meters

Therefore, the length of the rectangle is 12 meters and the width is 8 meters.

Answer 2

The formula for the area of a rectangle is Response area

Answer 3

[AI-generated answer — Bot GPT 3.5]

The formula for the area of a rectangle is:

\[ \text{Area} = \text{length} \times \text{width} \]

or simply,

\[ A = lw \]

Answer 4

Using trial and error, if the area is 96 m^2, then the length and width are

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the length and width using trial and error, we know that the area is 96 m^2. We can start by trying different combinations of length and width that multiply to give 96.

Let's start with some pairs of factors of 96:

1. 1 x 96
2. 2 x 48
3. 3 x 32
4. 4 x 24
5. 6 x 16
6. 8 x 12

Since the length is four meters less than twice the width, we can try these pairs of factors in the equation L = 2w - 4 to see if it holds true.

Let's start with the last pair:

For width = 8, the corresponding length would be:
L = 2(8) - 4 = 16 - 4 = 12

So, the length is 12 meters and the width is 8 meters, which satisfies the conditions given in the question. Therefore, the length and width of the rectangle are 12 meters and 8 meters, respectively.